Question

The base radius and height of a cone is 5cm and 25cm respectively. if the cone is cut parallel to its base at a height of h from the base. if the volume of this frustum is 110cm cubic.find the radius of smaller cone?

Answer 1

Answer: The radius of smaller cone would be 4.7 cm.

Step-by-step explanation:

Dimensions of bigger cone is given by:

R= 5cm

H= 25cm

Dimension of smaller cone would be:

Radius= r

Height= 25-h

We know both the cones are similar, so the ratio of corresponding sides would be equal.

r/R=(25-h)/H

25-h=r*H/R=r*25/5=5r

So,

The volume of the frustum= volume of bigger cube - volume of smaller cube= 1/3*pi*(R^2*H-r^2(25-h))

110= 1/3*22/7*(5^2*25-r^2*5r)

105= 625-5r^3

5r^3=625-105=520

r^3=104

Taking cube root, we get

r= 4.7cm