FORMULA FOR A CUBOID
Let the length, breadth and height of a cuboid be l, b and h units respectively. Then, we have the following:
1) Volume= Area of the base x Height
= Length x Breadth x Height
= lbh cubic units
EXERCISE -A
1) Find the volume of the cuboid of the following:
A) length= 30cm, breadth=24cm, height= 18cm. 12960 cm³
B) length= 20cm, breadth=14cm, height= 8cm. 2240 cm³
C) length= 3m, breadth=10cm, height= 10cm. 30000cm³
D) Area of the base= 20 cm², height = 20 cm. 400 cm³
E) Find the capacity of the tank in litres whose length, breadth and height are 3.5m, 4m, 6.2 m. 86800 lit.
F) Find the capacity of the tank in litres whose length, breadth and height are 3cm, 4cm, 6cm. 0.72 lit.
EXERCISE -B
1) a) length= 5m, breadth=4m, volume= 160m. Find height. 8 m
b) breadth=40cm, height= 1cm, volume= 1000 cm³ find length. 25 cm
c) volume= 300m, breadth=20 cm, height= 15cm. Find length 100 cm
d) The volume of a cuboid is 440cm³ and the area of its base is 88 cm². Find its height. 5 cm
e) Find the height of a cuboid whose base area is 216 cm² and volume is 1080cm³. 5cm
f) Find the height of a cuboid whose volume is 312 cm³ and base area is 26cm². 12cm
g) A rectangular water reservoir contains 105 m³ of water. Find the depth of the water in the reservoir if its base measures 12m by 3.5m. 2.5m
h) A rectangular water Reservoir contains 105m³ of water. Find the depth of the water in the Reservoir if it's base measures 12m by 3.5 m. 2.5m
i) Capacity of a water tank is 420kL. If the length and breadth of the tank are respectively 7m and 6m, find its depth. 10m
EXERCISE - C
1) a) length, breadth and height of the cuboid are in ratio 3:5:6 and the volume is 720cm³. Find the dimensions of the cuboid. 6cm, 10cm, 12cm
b) length, breadth and height of the cuboid are in ratio 1:4:5 and the volume is 20cm³. Find the dimensions of the cuboid. 1, 4, 5 cm
c) A cuboid whose length is 5m and ratio of breadth and height are in ratio 3:4. If the volume is 240 m³. Find breadth and height. 6m, 8m
d) The breadth of a room is twice its height, and length is three times of height and the volume of the room is 162dm³. Find its dimensions. 9,6,3
h) The breadth of a room is twice its height, one half of its length and the volume of the room is 512 dm³. Find its dimensions. 16dm, 8cm,4dm
e) If length of the cuboid is double then width and width is double then height and volume is 8000 cm³, then their dimensions. 40cm,20cm,10cm
EXERCISE -D
1) a) The dimensions of a cinema hall are 100m, 50m and 18m. How many persons can sit in the hall, if each person requires 150m³ of air ? 600
b) A granery is in the shape of a cuboid of size 8m x 6m x 3m. If a bag of grain occupies a space of 0.65 m³, how many bags can be stored in the granary? 221 bags
d) A godown is in the form of a cuboid of measures 55m x 45m x 30 m. How many cuboidal boxes can be stored in it if the volume of one box is 1.25 m³? 59400
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c) How many planks each of which is 2m long, 2.5cm broad and 4cm thick can be cut off from a wooden block 6m long, 15 cm broad and 40 cm thick ? 180
e) An agricultural field is in the form of a rectangle of length 20m and width 14m. A pit 6m long, 3m wide and 2.5m deep is dug in a corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the field. Find the extent to which the level of the field has been raised. 17.18 cm
) h) A field is in the form of a rectangle of 18m long and 15m wide. A pit, 7.5m long, 6m broad and 0.8m deep in a corner of the field and the earth taken out is spread over the remaining area of the field. By how much the level of field is raised? 16cm
j) The dimensions of a field are 12m by 10m. A pit 5m long, 4m wide and 2m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. Calculate by how much is the level of the field raised? 40cm
k) A rectangular tank measuring 5m x 4.5 m x 2.1m is dug in the centre of the field measuring 13.5m x 2.5 m. The earth dug out is spread evenly over the remaining portion of the field. How much is the level of the field raised ? 4.2m
l) A pit is dug in the shape of a cuboid with dimensions 10m x 8m x 3m. The earth taken out is spread evenly on a rectangular plot of land with dimensions 40m x 30m. The earth taken out is spread evenly on a rectangular plot of land with dimensions 40m x 30m. What is increase in the level of the plot ? 20
f) A field is 200m long and 150m broad. There is a plot, 50m long and 40m broad, near the field. The plot is dug 7m deep and the earth taken out is spread evenly on the field. By how many metres is the level of the field raised? Give the answer to the second place of decimal. 0.47 m
g) A field is 150m long and 120m wide. A plot (outside the field) 50m long and 30m wide is dug to a depth of 8m and the earth taken out from the plot is spread evenly in the field. By how much the level of field is raised? 8 cm
i) A rectangular pit 1.4m long, 90m broad and 70 cm deep was dug and 1000 bricks of base 21cm by 10.5 cm were made from the earth dug out. Find the height of each brick. 4cm
m) A teak wood log is cut first in the form of a cuboid of length 2.3m, width 0.75m and of a certain thickness. Its volume is 1.104 m³. How many rectangular planks of size 2.3m x 0.75 m x 0.04 m can be cut from the cuboid? 16
n) Water in a canal, 30dm wide and 12 dm deep, is flowing with a velocity of 20 km per hour. How much area will it irrigate in 30 min if 9 cm of standing water is desired? 400000 m²
o) A rectangular reservoir is 120m long and 75m wide. At what speed per hour must water flow into it through a square pipe of 20cm wide so that the water rises by 2.4m in 18 hours. 30 km/hr
p) Water flows in a tank 150m x 100m at the base, through a pipe whose cross section is 2dm by 1.5dm at the speed of 15km per hour. In what time, will the water be 3m deep ? 100 hours
q) A rectangular tank is 80m long and 25m broad. Water flows into it through a pipe whose cross section is 25 cm², at the rate of 16 km per hour. How much the level of the water rises in the tank in 45 minutes. 1.5 cm
r) Water in a rectangular reservoir having base 80m by 60m is 6.5m deep. In what time can the water be emptied by the pipe at the rate of 15 km/hr? 52 hrs
s) A river 2.5m deep and 44m wide is flowing at the rate of 2.4km per hour. How much water runs into the sea per minute? 4400 m³
t) Water in a canal 30dm wide and 12dm deep is flowing at the rate of 100km per hour. How much area will it irrigate in 30 minutes if 8cm of standing water is desired? 225000 m²
EXERCISE - E
Find the surface area:
1)a) length 30cm, breadth=24cm, height= 18cm. 3384 cm²
b) length 36cm, breadth=30cm, height= 24cm. 5328 cm²
c) length is 16cm, breadth 15cm and length 8.5cm. 1007cm²
d) 5m by 4m by 3m. 94m²
e) Find the surface area of the cuboid whose length is 16cm, breadth 15cm and length 8.5cm. 1007cm²
EXERCISE - F
1) The surface area of a cube is 384cm². Find
A) the length of the edge. 8cm
B) volume of the cube. 512 cm²
b) A closed rectangular box has inner dimensions 90cm by 80cm by 70 cm. Find the area of tin-foiled needed to line its inner surface. 38200 cm²
c) The length, breadth and height of a cuboid are in the ratio 7:6:5. If the surface area of the cuboid is 1926 cm². Find the dimensions and volume. 21cm, 18cm,15cm, 5670 cm³
d) e) The volume of a cuboid is 448cm³. Its height is 7cm and the base is a square. Find
A) a side of the square base. 8cm
B) surface area of the cuboid. 352cm²
e) The length, breath and height of a rectangular solid are in the ratio 5:4:2. If its total surface area 1216cm². Find the volume of the solid. 2560cm³
f) the volume of a cube is 729cm³, then find its surface area. 486 cm²
g) A closed rectangular wooden box has inner dimension 90cm by 80cm by 70cm. Compute its capacity and the area of the tin foil needed to line its inner surface.
h) The lateral surface area of a cuboid is to 224 cm². Its height is 7 cm and the base is a square. Find
A) a side of the square base.
B) the volume of the cuboid.
EXERCISE - G
1) Find the length of the longest rod that can be placed in a room 12m long, 9m broad and 8m high. 17m
2) Find the length of the longest pole that can be put in a room of dimensions 10 m x 10m x 5m. 15 m
3) Can a pole 6.5m long fit into the body of a truck with internal dimensions of 3.5m, 3m, and 4m ?
4) A solid piece of metal, cuboidal in shape, with dimensions 24cm, 18cm and 4cm. Find its
A) volume. 432 cm³
B) Lateral surface area. 336 cm²
C) Area of 4 faces. 336 cm²
D) Total surface area. 1200 cm²
E) Diagonal. 30.26 cm
5)
EXERCISE - H
1) One edge of a cube is 7cm Find
A) surface area. 294 cm²
B) volume. 343 cm³
C) diagonal. 7√2
2) The diagonal of a cube is √12cm, what is its edge? 2cm
3) find the volume of a cube (in cubic metres)whose diagonal is 2.5m. 3.01m³
4) If the lateral surface area of a cube is 100 cm², find its volume. 125 cm³
5) The volume of a cube is 343 cm³, find the length of an edge of cube. 7cm
6) If each edge of a cube is tripled, then find how many times will its volume become? 27 times
7) If the length of the side of a cube is doubled, than find the ratio of the volume of new cube and original cube. 8:1
b) A rectangular room is 4.5 long, 4m wide and 3m high. Find the cost of white washing its walls and and the roofs at ₹7.50 per square metre. ₹517.50
c) Three cubes each of side 8cm are joined together side by side to form a cuboid. Find the surface area of the cuboid. 896 cm²
d) An aquarium is in the form of a cuboid whose external measures are 70 cm x 28cm x 35cm. The base, side faces and back face are to be covered with coloured paper. Find the area of the paper needed. 6370cm²
d) A suitcase with measures 80cm x 48cm x 24cm is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96cm is required to cover 100 such suitcases? 144m
) The internal dimensions of a rectangular room are 6m, 5m and 3.5m. It has two doors of size 1.2m by 2m and three windows of size 1m by 1.9 m. The walls of the room are to be prepared with a wallpaper of width 70 cm. Find the cost of the paper at the rate of ₹6.50 per metre. ₹ 617.50
) The internal dimensions of rectangular hall is 15mx 12m x 4m. There are 4 windows each of dimension 2m x 1.5m and 2 doors each of dimension 1.5m x 2.5m. Find the cost of white washing all four walls of the hall, if the cost of whitewashing is ₹5 per m². What will be the cost of white washing if the ceiling of the hall is also white washed? ₹982.50, ₹1882.50
) A swimming pool is 50m in length, 30m in breadth and 2.5m in depth. Find the cost of cementing its floor and walls at the rate of ₹27 per square metre. ₹52300
) The floor of a rectangular hall has a parimeter 236m. Its height is 4.5m. Find the cost of painting its four walls (doors and windows be ignored) at the rate of ₹8.40 per m². ₹8920.80
) A cuboidal fish tank has a length 30cm, a breadth of 20cm and a height is 20cm. The tank is placed on a horizontal table and it is three-quarters full of water. Find the area of the tank which is in contact with water. 2100 cm²
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) A rectangular room is 6m long, 5m wide and 3.5m high. it has two doors of size 1.1m by 2m and 3 windows of size 1.5m by 1.4m. Find the cost of white washing the walls and the ceiling of the room at the rate of ₹5.30 per m³. ₹510.39
) A cuboidal block of metal has dimensions in 36cm by 32cm by 0.25m. it is melted and recast into cubes with edge 36cm by 32cm by 0.25m. it is melted and recast into cubes with an edge of 4 cm.
A) How many such cubes can we made ? 450
B) what is the cost of silver coating surface of the cubes at the rate of ₹0.75 per square centimetre ? ₹324003
) Three Cubes of silver with edges 3cm, 4cm, 5cm are melted and recast into a single cube. Find the cost of coating the surface of the new cube with gold at the rate of ₹3.50 per cm². ₹756
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) If the dimensions of a rectangular room is 10m x 12m x 9m, then find the cost of painting its four walls at the rate of 8 per m². ₹3168
) The length of a room is 50% more than its breadth. The cost of carpenting the room at the rate of ₹38.50m² is ₹924 and the cost of papering the walls at ₹3.30m² is ₹240.50. if the room has one door of dimensions 1m x 2m and two Windows each of dimension 1m x to 1.5m, find the dimension of the room.
) Preeti is painting the walls and ceiling of a hall whose dimension are 18m x15m x 5m. From each can a paint 120 m² of area is painted. How many cans of paint she need to paint the hall ?
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) The inner dimension of a closed wooden box are 2m by 1.2m by 0.75 m. The thickness of the wood is 2.5cm. Find the cost of wood required to make the box. If 1 m³ if wood costs ₹ 5400.
) the length, breath and height of cuboidal water tank is 7m, 6m and 2m respectively. If 4200 litre of water is pumped out from the tank. Find the fall in water level in the tank.
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) The external dimensions of an open rectangular wooden box are 98cm by 84cm by 77cm. If the wood is 2cm think all around, find
A) The internal dimensions of the box. 94, 80, 75cm
B) the capacity of the box. 56400cm³
C) the volume of the wood used in making the box. 69864cm³
D) weight of the box in kilogram correct to 1 decimal place, given that 1 cm³ of wood weight 0.8g. 55.9 kg
) A closed box is made of 2cm thick wood with external dimensions 84cm x 75 cm x 64 cm. Find the volume of the wood required to make the box. 62400 cm³
) Water is pouring into a cuboidal reservoir at the rate of 40 litres per minute. If the capacity of reservoir is 84 m³, find the number of hours it will take to fill the reservoir. 35 hours
B
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EXERCISE - B
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5)
6) If V is the volume of a cuboid of a dimension a,b,c and S is its surface area, then prove that 1/V= 2/S(1/a+ 1/b + 1/c)
7) The areas of the three adjacent faces of a cuboid are x,y and z. If the volume is V, prove that V²= xyz
9) cubes A,B,C having edges 18cm, 24cm and 30cm respectively are melted and moulded into a new cube D. Find the edge of the bigger cube D. 36cm
10)
11) A closed iron tank 12m long, 9m wide and 4m deep is to be made. Determine the cost of iron sheet used at the rate of ₹5 per metre sheet, sheet being 2m wide.
₹960
12) A tank open at the top is made of iron sheet 4m wide. If the dimensions of the tank are 12m x 8m x 6m, find the cost of iron sheet at ₹17.50 per metre. 1470
13) Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of three cubes. 7:9
14) A river 2.5m deep and 44m wide is flowing at the rate of 2.4 km per hour. How much water runs into the sea per minute ? 4400m²
15) Water in a Canal 30dm wide and 12 dm deep, is flowing with a velocity of 100 km per hour. How much area will it irrigate in 30 minutes if 8cm of standing water is desired? 225000m²
16) The dimensions of a room are 12.5m by 9m by 7m. There are 2 doors and 4 Windows in the room; each door measures 2.5m by 1.2m and each window 1.5m by 1m. Find the cost of painting the walls at ₹3.50 per square metre. ₹1011.50
17) A field is 200m long and 150m broad. There is a plot, 50m long and 40m broad, near the field. The plot is dug 7m deep and the earth taken out is spread evenly on the field. By how many metres is the lavel of the field raised? Give the answer to the second place of decimal. 0.47m
18) A field is 150m long and 100m wide. A plot (outside the field) 50m long and 30m wide is dug to a depth of 8m and the earth taken out from the plot is spread evenly in the field. By how much the level of field is raised? 8cm
19) A field in the form of a rectangle of length 18m and the width 15m. A pit, 7.5m long, 6m broad and 0.8m deep, is dug in a corner of the field and the earth taken out is spread over the remaining area of the field. Find out the extent to which the level of the field has been raised. 16cm
20) The dimensions of a field are 12m by 10m. A pit 5 metre long. 4 metre wide 2 metre deep is dug in one corner of the field and the earth removed had been evenly spread over the remaining area of the fielder. Calculate by how much is the lavel of the field raised? 40cm
21) Three metal cubes with edge 6cm, 8cm and 10cm respectively are melted together and formed into a single cube. Find the volume, surface area and the diagonal of the new cube. 1728cm³, 864cm², 12√3 cm.
22) Two cubes whose edges measure 3cm, 4cm, and 5cm respectively are melted to form a new cube. Find the surface area of the new cube formed. 216
23) Two cubes each of the volume 512cm³ are joined end to end. Find the surface area of the resulting cuboid. 640cm²
24) A 4 cm cube is cut into 1cm cubes. Calculate the total surface area all the small cubes. 384cm²
25) Half cubic metre of gold sheet is extended by hammering so as to cover an area of 1 hectare. Find the thickness of the gold sheet. 1/200 cm
26) The cost of preparing the walls of a room 12 metre long at the rate of ₹1.35 per square metre is ₹340.20 and the cost of matting the floor at 85 paise per square metre is ₹91.80. Find the height of the room. 6m
27) The length of a hall is 18m and the width 12 metre. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of a wall. 7.2m
28) A rectangular tank is 80m long and 25 metre broad. Water flows into it through a pipe whose cross section is 25cm², at the rate of 16 km per hour. How much the level of the water rises in the tank in 45 minutes. 1.5m
29) Water in a rectangular reservoir having base 80m by 60m is 6.5m deep. In what time can the water be emptied by a pipe of which the cross section is a square of side 20cm, if the water runs through the pipe at the rate of 15km/hr? 52 hrs
30) A metal cube of edge 12cm is melted and formed into three smaller cubes. If the edges of the two smaller cubes are 6cm and 8cm. Find the edge of 3rd smaller cube. 10cm
31) Given that 1cm³ of marble weight 25 kg, the weight of a marble block 28 cm in width and 5 cm thickis 112 kg. Find the length of the block. 32cm
32) The dimensions of a cinema hall are 100m, 50m and 18m. How many persons can sit in the hall, if each person requires 150m³ of air. 600
33) The dimensions of an open box are 50cm x 40cm x 29cm. Its thickness is 2cm. If cubic centimetre of metal used in the box weighs 0.5 gram, find the weight of the empty box. 6832
34) An open box is made of wood 3 cm thick. Its external length, breadth and height are 1.48m, 1.16m and 8.3dm. Find the cost of painting the inner surface at ₹50 per sq.metere. 32cm
35) A box with lid is made of 2cm thick wood. Its external length, breadth and height 25cm, 18cm and 15cm respectively. How many cubic cm of a liquid can be placed in it ? Also find the volume of the wood used in it. 3234cm³, 3516
36) The external dimension of a closed wooden box are 48cm, 36cm, 30cm. The box is made of 1.5cm thick wood. How many bricks of size 6cm x 3cm x 0.75cm can be put in the box ? 6.2970
37) How many cubic centimetres of iron hard there in an open box whose external dimensions are 36cm, 25cm and 16.5cm, the iron being 1.5cm thick throughout? if one cubic centimetre of iron weight 15 gram, find the weight of the empty box in kg. 3960cm³, 59.4kg
38) The dimensions of a rectangular box are in the ratio 2: 3:4 and the difference between the cost of covering it with sheet of paper at the rates of ₹8 and ₹9.50 per m² is ₹1248. Find the dimensions of the box. 8,12,16
39) The length and the breadth of a hall are in the ratio 4:3 and its height is 5.5 metres. The cost of decorating its walls (including doors and windows) at ₹6.60 per square metre is ₹5082. Find the length and the breadth of the room. 40m, 30m
40) Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube. 125
41) A cube of 9cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 15cm and 12cm. Find the rise in water level in the vessel. 4.05cm.
42) A rectangular container whose base is a square of side 5c, stands on a horizontal table, and holds water up to 1 centimetre from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic centimetre of water overflows. Calculate the volume of the cube and also the length of its edge. 27cm³, 3cm
43) The volume of a cuboid is 440 cm³ and the area of its base is 88 cm². Find its height. 5cm
44) A cube of 9cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base 15cm and 12cm, find the rise in water level in the vessel. 4.05cm
45) The length of a cold storage is double its breadth. Its height is 3 metres. The area of its 4 walls (including doors) is 108 m². Find its volume. 216m³
46) The cubes each of 10cm edge are joined end to end. Find the surface area of the resulting cuboid. 1000cm²
47) Three cubes whose edges measure 3cm, 4cm and 5cm respectively to form a single cube. Find its edge. Also, find the surface area of the cube. 216cm²
48) The sum of Length, breadth and depth of a cuboid is 19cm and the length of its diagonal is 11cm. Find the surface area of the cuboid. 240 cm²
49) A plot of land in the form of a rectangle has a dimension 240m x 180m. A drainlet 10 metre wide is dug all around it (on the outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25cm. Find the depth of the drainlet. 1.227 m
50) Three cubes each of side 5 cm are joined end to end. Find the surface area of the resulting cuboid. 350 cm²
51) Find the number of bricks, each measuring 25cm x 12.5cm x 7.5 cm required to construct a wall 6 m long, 5m high and 0.5m thick, while the cement and sand mixture occupies 1/20 of the volume of the wall. 6080
52) A metallic sheet is of the rectangle shape with dimensions 48cm x 36cm. From each one of its corners, a square of 8cm is cutoff. An open box is made of the remaining sheet. Find the volume of the box. 5120 cm³
53) How many plants each of which is 2 metre long, 2.5 cm broad and 4 cm thick can be cut off from a wooden block 6 metre long, 15cm broad and 40 cm thick ? 180
54) An agricultural field is in the form of a rectangle of length 20m and width 14m. A pit 6m long, 3 metre wide and 2.5 m deep is dug in a corner of the field and the earth taken out of the pit is a spread uniformly over the remaining area of the field. Find the extent to which the level of the field has been raised. 17.18 cm
55) A tank wood log is cut first in the form of cuboid of length 2.3m, width 0.75m and of a certain thickness. Its volume is 1.104m³. How many rectangular planks of size 2.3m x 0.75m x 0.04m can be cut from the cuboid? 16
56) A reservoir is in the form of a rectangular parallelopiped (cuboid). Its length is 20m. If 18 kl of water is removed from the reservoir, the water level goes down by 15cm. Find the width of he reservoir (1kl= 1m³). 6m
57) The length of a hall is 20 metre and width 16m. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height and the volume of the hall. 8.88m, 2844.4 m³
58) A granary is in the shape of a cuboid of size 8m x 6m x 3m. If a bag of the grain occupy a space of 0.65m³, how many bags can be stored in the granary. 221
59) A class room is 7m long, 6.5m wide and 4m high. It has one door 3m x 1,4m and 3 windows, each measuring 2m x1m. The interior walls are to be colour washed. The contractor charges ₹5.25 per sq.m. Find the cost of colour washing. ₹513.45
60) A room is half As long again as it is bread. The cost of carpeting the room at ₹3.25 per m² is ₹175.50 and the cost of papering the walls at ₹1.40 per m² is ₹240.80. If one door and 2 windows occupies 8 m², find the dimensions of the room. 9,6,6m
61) The cost of paparing four walls of a room at 70 paise per square metre is ₹157.50. The height of the room is 5 metres. Find the length and the breadth of the room if they are in the ratio 4:1. 18m, 4.5m
62) A solid cube is cut into two cuboid of equal volumes. Find the ratio of the total surface area of the given cube and that of one of the cuboid. 3:2
63) Water in a Canal, 30dm wide 12 dm deep, is flowing with a velocity of 20 km per hour. How much area will it irrigate 30mins if 9cm of standing water is desired? 400000m²
64) A rectangular reservoir is 120m long and 75 metre wide. At what speed per hour must water flow in to it through a square pipe of 20 cm wide so that the water rises by 2.5m in 18 hrs. 30km/hr
65) A rectangular tank measuring 5m x 4.5 my 2.1m is dug in the centre of the field measuring 13.5 m x 2.5m. The earth dug out is spread evenly over the remaining portion of the field. How much is the level of the field raised? 4.2m
66) A rectangular water is reservoir is 10.8m by 3.75m at the base. Water flows into it at the rate of 18m per second through a pipe having the cross section 7.5 cm x 4.5cm. Find the height to which the water will rise in the reservoir in 30 minutes . 2.7m
67) Water flows in a tank 150m x 100m at the base, through a pipe whose cross section is 2dm by 1.5dm at the speed of 15 km per hour. In what time, will the water be 3 metres deep? 100 hours
68) A rectangular tank is 225m by 162m at the base. With what speed must water flow into it through an aperture 60cm by 45cm that the lavel may be raised 20cm in 5 hours. 5400 m/hr
69) The external length, breadth and height of a closed rectangular wooden box are 18cm, 10cm and 6cm respectively and thickness of wood is 1/2cm. When the box is empty, it weights 15 kg and when filled with sand it weighs 100 kg. Find the weight of the cubic cm of wood and cubic cm of sand. 1/21kg, 1/9 kg
70) The outer dimensions of closed wooden box are 10cm by 8cm by 7cm. Thickness of the wood is 1 centimetre. Find the total cost of wood required to make box if 1cm³ of wood cost ₹2.00. ₹640
71) The dimensions of a rectangular box are in the ratio 2:3:4 and the difference between the cost of covering it with sheet of paper at the rate of ₹4 and ₹4.50 per square metre is ₹460. Find the dimensions of the box. 8, 12, 16m
g) Area of three faces of a box are 120cm², 72cm² and 60cm². What is the volume of the box 720 cm³
g) A reservoir is in the form of a rectangular parallelopiped(cuboid). Its length is 20m. If 18 kl of water is removed from the reservoir, the water level goes down by 15cm. Find the width of the reservoir (1 kl= 1 m³). 6m
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