Question

a cone of height = 24 cm and radius of base is 6 cm is made up of clay if we reshape it into the sphere find the radius of the sphere

Answer 1

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Answer 2

Formula used:

$\boxed{\boxed{\large\mathbf{Volume \: of \: Cone = \frac{1}{3}π{r}^{2}h}}}$

$\boxed{\boxed{\large\mathbf{Volume \: of \: Sphere = \frac{4}{3}π{r}^{3}}}}$

Given,

$\bf Height \: of \: Cone = 24 \: cm \\ \bf Radius \: of \: the \: Base = 6 \: cm$

Since, The Cone is being reshaped into a Sphere
Hence, The Volume of Cone = The Volume of Sphere.

$\frac{1}{3} \pi {r}^{2} h = \frac{4}{3 } \pi {r}^{3} \\ \\ \frac{1}{3} \pi( {r}^{2} h) = \frac{1}{3} \pi(4 {r}^{3} ) \\ \\ {r}^{2} h = 4{r}^{3} \\ \\ \bf Putting \: the \: given \: values \\ \\ {(6)}^{2} \times 24 = 4 {r}^{3} \\ \\ {r}^{3} = \frac{36 \times 24}{4} \\ \\ {r}^{3} = 18 \times 12 \\ \\ {r}^{3} = 216 \\ \\ r = \sqrt[3]{216} \\ \\ \bf It \: can \: be \: written \: as \\ \\ r = \sqrt[3]{ {(6)}^{3} } \\ \\ \bf r = 6cm$

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