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.



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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