Question

A spherical ball of 8 cm diameter is melted into a cone with base 20 cm in diameter. Find its height.

Answer 1

area of spherical ball = pie x r square

                                  =22/7 * 4 = 12.57

area of spherical ball = area of cone = 1/2 * radius * height

12.57 = 1/2 * 10 * h

h = 12.57 * 2 /  10

h = 2.514 cm

Answer 2

This is a question testing the concept of volume.

The formulas are as below:

Sphere Volume = 4/3πr³

Volume of a cone = h/3πr²

The radius of the spherical ball = 8/2 = 4 cm

The volume of the spherical ball :

= 4/3 × 3.14 × 4² = 66.99 cm³

the volume of a cone = volume of the spherical ball.

radius of the cone = 20/2 = 10 cm

66.99 = 1//3 × 10² × h

66.99 = 33.33h

h = 66.99/33.33

h = 2.01 cm