# A Cone of Height 20 Cm and Radius of Base 5 Cm is Made up of Modeling Clay. a Child Reshapes It in the Form of a Sphere. Find the Diameter of the Sphere. - Mathematics

A cone of height 20 cm and radius of base 5 cm is made up of modeling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.

#### Solution

Let the radius of the sphere be r

Radius of the cone = 5 cm

Height of the cone = 20 cm

Since the cone is reshaped to form a sphere, the volumes of the sphere and the cone are equal.

∴ 4/3pir^3=1/3pi(5cm)^2xx(20 cm)              (∵ \text{Text of cone =}1/3 piR^2H)

rArr r^3=125 cm^3

rArr r^3=(5 cm)^3

rArr r^3=5 cm

Therefore, diameter of the sphere = 2r = 2 × 5 cm = 10 cm

Concept: Frustum of a Cone
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