Question

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Answer 1

Volume of cone

$= \frac{1}{3} \times 6 \times 6 \times 24 \: {cm}^{3}$

If r is the radius of the sphere

Volume of sphere is

$= \frac{4}{3} \pi {r}^{3}$

Volume of clay remains same both in cone and sphere shape

$\frac{4}{3} \pi {r}^{3} = \frac{1}{3} \times 6 \times 6 \times 24$

${r}^{3} = 3 \times 3 \times 24$

$r = 6 \: cm$

The radius of sphere is 6 cm

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Answer 2

Answer:

The height of the cone =h=24 cm

and the radius of the cone=r=6cm

$∴ volume \: of \: cone = \frac{1}{3} \pi {r}^{2} h$

$= \frac{1}{3} \pi \times {6}^{2} \times 24 {cm}^{3}$

let the radius of the reshaped sphere be r

$then \: the \: volume \: of \: sphere = \frac{4}{3} \pi {r}^{3}$

As the cone of clay is reshaped in sphere so the volume of two should be same

$∴  \frac{4}{3}\pi {r}^{ 3} = \frac{1}{3} \pi \times {6}^{2} \times 24$

${r}^{3 } = \frac{\pi \times 6 \times 6 \times 24}{4\pi} = {6}^{3}$

$r = 6cm$

Hence,the radius of required sphere =6cm