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.
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=12πh⇒h=512×2π12×3π=2569=28.44 cm
∴Height of the cone, h=28.44 cm