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

Question 25 Mensuration Exercise 17.5

A solid metal cylinder of radius 14 cm and height 21 cm is melted down and recast into spheres of radius 3.5 cm.

Calculate the number of spheres that can be made.

Solution:

No matter how different the new shape is, when we change one solid shape into another, its volume stays the same. In fact, the volume of the cylinder is equal to the sum of the volumes of the smaller spheres formed by melting one large cylinder into numerous smaller ones.

Given radius of the metal cylinder, r = 14 cm

Height of the metal cylinder, h = 21 cm

Radius of the sphere, R = 3.5 cm

Volume of the metal cylinder =π r2h

= (22/7)×142×21

= 22×2×14×21

= 12936 cm3

Volume of sphere = (4/3)π R3

= (4/3)×(22/7)×3.53

= 11×49/3

= 539/3 cm3

Number of spheres that can be made = Volume of the metal cylinder/ Volume of sphere

= 12936 ÷539/3

= 12936 ×3/539

= 72

Hence the number of spheres that can be made is 72.

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