Question

from a right circular cone of radius 12 cm and height 20 CM a small cone of radius 3 cm from the top and parallel to the base is cut off and removed . Find the ratio of volume of smaller cone and the volume of frustum of cone obtained​

Answer 1

from a right circular cone of radius 12 cm and height 20 CM a small cone of radius 3 cm from the top and parallel to the base is cut off and removed .

Given,

h = 20 cm

r1 = 12 cm

r2 = 3 cm

Volume of frustum of cone

V = (1/3) × π × h × (r1² + r2² + (r1 × r2))

V = (1/3) × (22/7) × 20 × (12² + 3² + (12 × 3))

V = 440/21 × (144 + 9 + 36)

Vf = 3960 cm³

Volume of the cone

V = 1/3πr²h

h2 = r2 × h1 / r1

h2 = 3 × 20 / 12

h2 = 5 cm

Volume of smaller cone

V = 1/3 × 22/7 × 3² × 5

V = 22 × 3 × 5 / 7

V = 330 / 7 cm³

The ratio of volume of smaller cone and the volume of frustum of cone obtained​ is given by,

V / Vf = (330/7) / 3960

V / Vf  = 12 / 7