ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration

Question 7 Mensuration Exercise 17.5

The volume of a cone is the same as that of the cylinder whose height is 9 cm and diameter 40 cm. Find the radius of the base of the cone if its height is 108 cm.



Volume is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. Sometimes, volume is also termed as capacity.

Given height of the cylinder, h = 9 cm

Diameter of the cylinder = 40 cm

Radius of the cylinder, r = 40/2= 20 cm

Volume of the cylinder =π r2h

= π 202×9

= π ×400×9

= 3600π cm3

Height of the cone, H = 108 cm

Volume of cone = (1/3)π r2h

= (1/3)π r2×108

= 36π r2

Since volume of cone is equal to the volume of the cylinder, we get

36π r2 = 3600π

r2 = 3600/36

r2 = 100

Taking square root on both sides,

r = 10 cm

Hence the radius of the cone is 10 cm.

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