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.



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. M L Aggarwal - Understanding ICSE Mathematics - Class 10 chapter Mensuration Question 4 Solution image

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