Question

A cone of radius 10cm is cut into two parts by a plane through the midpoint of its vertical axis parallel to it's base. Find the ratio of cone and frustum of a cone.

Answer 1

Dear Student

● Answer -

1/7

◆ Explanation -

Let h be height of the cone and given radius of base is 10 cm. When we cut the cone into 2, it turns it into cone and frustum.

For cut cone, radius is r/2 and height is h/2.

Volume of cut cone is -

Volume of cone = π(r/2)²(h/2)/3

Volume of cone = πr²h/24

For the frustum, two radii are r and r/2 and height is h/2.

Volume of frustum of cone is -

Volume of frustum = π(h/2)/3 [r² + (r/2)² + r(r/2)]

Volume of frustum = 7πr²h/24

Ratio of volume of cone to volume of frustum is -

V(cone)/V(frustum) = (πr²h/24)/(7πr²h/24)

V(cone)/V(frustum) = 1/7

Hence, Ratio of volume of cone to volume of frustum is 1/7.

Thanks dear...