Solid Geometry – Sectors cones

January 5, 2013 By K S Baskar 1 Comment

A sector of a circle of radius 5 cm is recast into a right circular cone of height 4 cm. What is the volume of the cone so formed?

Explanation:

A sector of a circle with radius 5 cm will look something like this.

When recast into a right-circular cone of height 4 cm it will look something like this.

Solid by rotation - sector to cone

Hence, the radius of the sector becomes the slant height of the cone. Therefore,

Base radius of the cone (r) = $\sqrt{l^{2} - h^{2}}$

Hence, r = $\sqrt{5^{2} - 4^{2}}$ = 3 cm.

Volume = (1/3)*pi*r2*h

= 12*pi cm³

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