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CONE

1) A cone of base radius 7cm and height 10cm. Find:

a) the volume 

b) the curved surface 

c) the total surface 

d) the mass, if material of the cone weighs 6gm per cm³

e) the cost, at the rate of Rs 3 per kg.

2) Find the curved surface of the following cones:

a) radius of base 5cm, slant height 7cm.

b) radius of base 3cm,  height 4 cm.

c) diameter of base 10cm, height 12cm

3) Find out whether the following statements is true or false:

The volume of cone is one half of the volume of the cylinder of the same radius and height.

4) Find the volume of the following cones:

a) radius of base 3cm, height 7 cm.
b) diameter of base 12cm, height 35 cm.

c) radius of base 5cm, slant height 23cm.

d) diameter of base 15cm, slant height 8.5cm

e) radius of base 13cm, height 6.3 dm

5) Find the curved surface of a cone, with radius of base 28cm and height 21cm.

6) Find the volume of a cone, with radius of base 35cm, slant height 37 cm.

7) Find the whole surface of a cone whose volume is 314.2cm³ and height 12 cm (π= 3.142).

8) What is the capacity of a cone whose base area is 154 sq.cm and height 12cm.

9) A right circular cone has radius of its base 30cm and slant height 50cm. Find its volume and total surface area.

10) Find the volume of a right circular cone, the diameter of whose base is 14cm and the area of curved surface is 550cm².

11) The height of a cone is 5m. Find the height of a cone sixteen times its volume and radius equal to its diameter.

12) How much canvas will it take to make a conical tent 11m in height and 12m in diameter at the base ?

13) The floor area of a tent in the form of a right circular cone is 3168/7 m². The canvas required for the tent is 3960/7 m². Find the air capacity of the tent.

14) Find the area to the nearest square metre of the canvas required to make a right circular conical tent 30m in perpendicular height and covering 1386 square metres of the ground. What is the cost to the nearest rupee of canvas required at the rate of Rs 4 per metres of width 1.5 metres?

15) A solid cone of base radius 6cm and height 10 cm is lowered into a cylindrical jar of radius 8cm, which contains water sufficient to submerge the cone completely. Find the rise in water level in the jar.

16) From a solid cylinder of height 12cm and base radius 5 cm a conical cavity of the same height and base is hollowed out. Find the surface area of the remaining solid.

17) A conical reservoir is 7m in diameter. Water is poured into it at the rate of 220 litres per minute. Find the height of water level in the reservoir after one hour. Give your answer to the nearest cm.

18) A cylindrical iron pillar 49 dm high and 6dm in radius is surmounted by a cone 14dm high. Find the volume of the pillar.

19) A girl fills a cylindrical bucket 32cm in height and 18cm in radius with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24cm, find 

a) the radius 

b) the slant height of the heap.

Give your answer correct to one place of decimal.

20) A rectangular vessel is 20cm x 16cm x 11cm and is full of water. This water is poured in to a conical vessel of base radius 10cm. If the vessel is completely filled, find the height of the vessel.

21) Find the volume of a right circular conical tent whose vertical height is 8m and the area of whose base is 156m².

22) The circumference of the base of a cone is 44cm and the height is 24cm, find 

a) the volume 

b) the slant height 

c) the curved surface area of the cone.

23) The height of a solid cylinder is 15cm and diameter 7cm. Two equal conical holes of radius 3cm and height 4cm are cut off. Find 

a) the volume 

b) the surface of the remaining solid.

24) The circumference of the base of a cone is 44cm and the slant height is 25cm. Find the volume and curved surface of the cone.

25) From a solid cylinder whose height is 8cm and radius is 6cm, a conical cavity of height 8cm and of base radius 6cm is hollowed out. Find the volume of the remaining solid correct to one place of decimal.

26) How many metres of cloth 1.1m wide will be required to make a conical tent, whose vertical height is 12cm and base radius is 16m ?  also, find the cost of the cloth at the rate of Rs 14/ metre.