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

Question 9 Mensuration Exercise 17.5

A metallic disc, in the shape of a right circular cylinder, is of height 2.5 mm and base radius 12 cm. Metallic disc is melted and made into a sphere. Calculate the radius of the sphere.

Solution:

When we convert one solid shape to another, its volume remains the same, no matter how different the new shape is.

Given height of the cylinder, h = 2.5 mm = 0.25 cm

Radius of the cylinder, r = 12 cm

Volume of the cylinder = π r2h

= π 122×0.25

= π 144×0.25

= 36 π cm3

Let R be the radius of the sphere.

Volume of sphere = (4/3)π R3

Since metallic disc is melted and made into a sphere, their volumes remains same.

(4/3)π R3 = 36π

R3 = 36×3/4

R3 = 27

Taking cube root

R = 3 cm

Hence the radius of the sphere is 3 cm.

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