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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. - CBSE Class 10 - Mathematics

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Question

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

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Solution 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. Concept: Frustum of a Cone.
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