This is the Important question of class 10 Based on Mensuration Chapter of M.L Aggarwal book for ICSE BOARD.
The radius of a solid metallic hemisphere is given, it is melted and recasted into right circular cone of base radius 6 cm. Find the height of the cone.
This is the Question Number 03, Exercise 17.5 of M.L Aggarwal.
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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.
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Given radius of the hemisphere, r = 8 cm
Volume of the hemisphere, V = (2/3)r3
= (2/3)×83
= (1024/3) 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)R2h = (1024/3)
(1/3)×62 ×h = (1024/3)
36h = 1024
h = 1024/36
= 28.44 cm
Hence the height of the cone is 28.44 cm.