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

Question 4 Mensuration Exercise 17.5

A solid metallic hemisphere of radius 8 cm is melted and recasted into right circular cone of base radius 6 cm. Determine the height of the cone.

Solution:

Even if the new shape may be different, when we change one solid shape into another, its volume stays the same.

Given radius of the hemisphere, r = 8 cm

Volume of the hemisphere, V = (2/3)π r3

= (2/3)π 83

= (1024/3) π cm3

Radius of cone, R = 6 cm

Since hemisphere is melted and recasted into a cone, the volume remains the same.

Volume of the cone, (1/3)π R2h = (1024/3)π

(1/3)×62 ×h = (1024/3)

36h = 1024

h = 1024/36

= 28.44 cm

Hence the height of the cone is 28.44 cm.

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