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Question 1
A solid metallic hemisphere of radius 8  cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.


Solution

Let height of the cone be h1
Given, radius of the base of the cone = 6 cm
Volume  of circular cone
=13πr2h=13π(6)2h=36πh3=12πh cm3

Also. Given radius of the hemisphere = 8 cm
Volume of the hemisphere=23πr3=23π(8)3=512×2π3

 Volume of the hemisphere=Volume of the cone

512×2π3=12πhh=512×2π12×3π=2569=28.44 cm

Height of the cone, h=28.44 cm


Mathematics
NCERT Exemplar
Standard X

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