SURFACE AREAS

AND VOLUMES

• Sum based on Cylinder

Q. The radius and height of a cylinder are in the ratio 3 : 7

and its volume is 1584 cm³. Find its radius.

Volume of cylinder = 1584 cm³

Sol.

1584 =

× (3x)²

× 7x

1584 =

22 ×

9 × x²

× x

1584

22 × 9

= x³

∴

x³ = 8

height (h) = 7x

x = 2

Radius (r) = 3x

= 3

× 2

= 6 cm

Radius of given cylinder is 6 cm

176

8

What is formula for finding volume of cylinder ?

πr²h

r : h = 3 : 7

Let the common multiple be ‘x’.

∴ Radius (r) = 3x ,

Volume of cylinder = πr²h

22

7

∴

∴

∴

∴

∴

1584 =

πr²h

∴

∴

r