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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration
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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.
Answer:
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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