Name: Conversion of Solids
Uploaded: 2019-07-19
Duration: 5 min 33 s
Description: What happens when a goldsmith heats a gold bar to create something? The gold bar's shape gets changed. But what about its volume? Does it change too? Find ou...

Question

A cone of height

24 cm

and radius of base

6 cm

is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

Accepted Answer

The height of the cone, $h = 24 cm$

The radius of the base of the cone, $r = 6 cm$

The volume of the cone $= \frac{1}{3} {(r)}^{2} h = \frac{1}{3} π {(6)}^{2} \times 24 {cm}^{3}$

Given that, a child reshapes the cone in the form of a sphere.

Let, the radius of the sphere is $r' cm$

So the volume of the sphere $= \frac{4}{3} π {(r')}^{3}$

Since the cone is reshaped into the sphere,

So, the volume of the sphere $=$ the volume of the cone

$∴ \frac{4}{3} π {(r')}^{3} = \frac{1}{3} π \times 6 \times 6 \times 24$

$\Rightarrow {(r')}^{3} = \frac{π \times 6 \times 6 \times 24 \times 3}{3 \times 4 \times π}$

$\Rightarrow r' = \sqrt[3]{6 \times 6 \times 6} = 6 cm$

Hence, the radius of the sphere is $6 cm$ .

A cone of height $24 cm$ and radius of base $6 cm$ is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

Important Questions on Surface Areas and Volumes

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