Question

A cone is 14 cm high and the radius of its base is 3.5 cm. It is melted and recast into a sphere. The radius of the sphere is :

Answer 1

Answer:

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Answer 2

Given⏩

Height of cone = 14cm

Radius of base = 3.5 cm

$volume \: of \: the \: cone = \frac{\pi {r}^{2} h}{3} = \frac{\pi {(3.5)}^{2} \times 14 }{3} {cm}^{3}$

Since , It is melted and recast into a sphere,

Solution⏩

Volume of sphere = Volume of the cone .

$\frac{4}{3} \pi {r}^{3} = \frac{\pi {(3.5)}^{2} \times 14 }{3} \\ = > {r}^{3} = \frac{\pi {(3.5)}^{2} \times 14 \times 3}{\pi \times 4 \times 3} \\ = > {r}^{3} = \frac{{(3.5)}^{2} \times 7}{2} = 42.875 \\ = > {r} = \sqrt[3]{42.875} = 3.5$

Hence , Radius of sphere = 3.5 cm