Magnus Academy (Maths Specialist): REVISION IX

CUBE CUBOID

1) Find the volume, the surface area and the diagonal of a cuboid 12cm long, 4 cm wide and 3cm high . 144,192,13

2) The volume of a cuboid is 440cm³ and the area of its base is 88cm². Find its height. 5cm

3) The volume of a cube is 1000cm. Find the total surface area. 600cm²

4) How many 3 metres cubes can be cut from a cuboard measuring 18m x 12m x 9m? 72

5) A cube of 9cm edge is immersed completely in a rectangular vessel containing water. If the dimension of the base 15cm and 12cm, find the rise in water level in the vessel. 4.05cm

6) The length of a cold storage is double its breadth . Its height is 3 meters. The area of its four walls (including doors) is 108 m². Find its volume. 216m³.

7) Two cubes each of 10 cm edge are joined end to end. Find the surface area of the resulting cuboid. 1000cm²

8) Three cubes edges measure 3cm, 4cm and 5cm respectively to form a single cube. Find its edge. Also find a surface area of the new cube . 6m, 216cm²

9) The sum of length, breath and depth of a cuboid is 19cm and the length of its diagonal is 11cm. Find the surface area of the cuboid. 240cm²

10) A plot of land in the form of a rectangle has a dimension 240m x 180m. A drainlet 10m 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 25 cm. Find the depth of the drainlet. 1.227

11) Three cubes each of side 5cm are joined end to end. Find the surface area of the resulting cuboid . 350cm².

12) Find the number of bricks, each measuring 25cm x 12.5 cm x 7.5 cm required to construct a wall 6m long, 5m high and 0.5m thick, while the cement and sand mixture occupies 1/20 of the volume of the wall. 6080

CIRCLE

1) Find the diameter circle whose circumference is 176m. 56m

2) A bicycle wheel makes 5000 revolutions in moving 11km. Find the diameter of the wheel. 70cm

3) A road which is 7m wide surrounds a circular park whose circumference is 352m. Find the area of the road. 2618 m²

4) Find the circumference of a circle of radius is 4.2cm. 26.4cm

5) Find the area of a circle of radius is 7.7cm. 186.34cm²

6) Find the length of the diameter of a circle whose circumference is 3.3m. 1.05m

7) Find the diameter of a circle whosrarea is 616m². 28m

8) Assuming that earth's equatorial diameter is 12530 km, find the circumference of the equator . 39380 km

9) Find the radius of a circle whose area is equal to the sum of the areas of three circles whose radii are 3cm, 4cm and 12cm. 13cm

10) The radius of a circle is 3m. What is the circumference of another circle, whose area is 49 times of the first ? 132m

11) A circular track has an inside circumference of 440m. if the which of the track is 7m, what is the outside circumference ? 484m

12) Find the area of a circular ring whose external and internal diameters of 20cm and 6cm respectively ? 286cm²

13) The wheel of a cart is making 2 revolutions per second. if the diameter of the wheel is 126cm, find its speed in km/hr. Give your answer, correct to the nearest km. 29 km/hr

14) How many times will the wheel of a car rotate in a journey of 1925m, if it is known that the radius of the wheel is 49cm ? 626 times

15) A garden roller has a circumference of 3 metres . How many revolutions does it make in moving 21 m ? 7 times

Continue......

PYTHAGORAS THEOREM

1) A right triangle has hypotenuse length p cm and one side of the length q cm. if p - q = 1, find the length of the third side of the triangle. √(2q +1) cm

2) The side of certain triangles are given below. Determine which of them are right angle triangles:

a) a=6cm, b= 8cm and c= 10 cm.

b) a= 5cm, b= 8cm, c= 11cm.

3) A man goes 10m due east and then 20m due north. Find the distance from the starting point. 26m

4) A ladder is placed in such a way that its foot is at a distance of 5m from a wall and its tip reachers a window 12m above the ground. Determine the length of the ladder . 13m

5) A ladder 25m long reaches a window of a building 20m above the ground. Determine the distance of the foot of the ladder from the building. 15m

6) A ladder 15m long reaches a window which is 9m above the ground on one side of a street. Keeping its foot at the same point , the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street. 21m

7) The hypotenuse of a right angle triangle is 6m more than the twice of the shortest side. if the third side is 2 m less than the hypotenuse, find the side of the triangle. 26,24 m

8) In figure ABC is a right angled at B. AD and CE are the two medians drawn from A and C respectively.

If AC= 5cm and AD= 3√5/2 cm, find the length of CE. 2√5 cm

9) In an equilateral triangle with side a, prove that

a) altitude =a√3/2

b) area= √3a²/4.

CHORD PROPERTY

1) The radius of a circle is 13 cm and the length of one of its chords is 10cm. Find the distance of the chord from the Centre. 12cm

2) Find the length of a chord which is at distance of 5cm from the centre of a circle of radius 13cm. 24cm

3) In the figure O is the centre of the circle of radius 5cm. OP perpendicular AB, OQ perpendicular CD, AB|| CD, AB= 6cm and CD= 8cm. Determine PQ. 1cm

4) In figure, O is the centre of the circle with radius 5cm,

OP perpendicular AB, OQ perpendicular CD, AB|| CD, AB= 6cm and CD= 8cm. Determine PQ. 7cm

5) PQ and RS are two parallel chords of a circle whose centre is O and radius is 10m. If PQ =16cm and RS= 12 cm, find the distance between PQ and RS, if they lie

a) on the same side of the centre O. 2

b) on opposite side of the centre O. 14

6) AB and CD are two parallel chords of a circle such that AB= 10cm and CD= 24cm. If the chords are on the opposite sides of the centre and the distance between them is 17cm. Find the radius of the circle. 13cm

7) AB and CD are two chords of a a circle such that AB =6cm, CD= 12cm and AB || CD. if the distance between AB and CD is 3cm, find the radius of the circle. 6.7cm

8) Two concentric circle Centre O have A, B, C, D as the point of intersection with the line l as shown figure.

If AD =12cm and BC= 8cm,, find the length of AB, CD, BD. 2, 2, 10cm

9) Two circles of radii 10cm and 8cm unterset and the length of the common chord is 12cm, Find the distance between the centres. 13.29

CIRCLE (MENSURATION)

1) The perimeter of the figure,

a semicircle described on AB as a diameter 7.2cm. Find r the radius of the semi circle. (π=22/7)

2) A. rectangular metal plate of the length 35 cm and of width 23cm has a circular hole of radius 7cm cut out. Find the area of the remaining portion of the plate. (π=22/7).

3) In the adjoining figure,

the area enclosed between the concentric circles is 770 cm². Given that the radius of the outer circle is 21cm, calculate the radius of the inner circle.

4) In the adjoining figure,

ABCD is a square inscribed in a circle of radius 7cm. Calculate

a) the area of the circle.

b) the area of the shaded portion. (π= 22/7)

5) ABCD is a square of side 4cm.

Find the area of the shaded portion . Use π=3.14 and give your answer correct to one places of decimal.

6) Find the perimeter of the quarter of the circle whose radius is 3.5cm, correct to one decimal place.

7) A copper wire when bent in the form of a square encloses an area of 121 cm². if the same wire is bent into the form of circle, find the area of the circle.

8) A road 3.5m wide surrounds a circular plot whose circumference is 44m. Find the cost of paving the road at Rs 10 per m².

9) The diameter represents the wiper of a car. With the dimensions given in the diagram,

calculate the shaded area swept by the wiper. (π=22/7).