Question

# A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is (a) 1.6 cm (b) 2.1 cm (c) 2.4 cm (d) 4.2 cm

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Solution

## (b) 2.1 cm Let r cm be the radius of the sphere. Radius of the base of the cone = 2.1 cm Height of the cone = 8.4 cm The cone is melted and recast into a sphere. Then volume of sphere = volume of cone $⇒\frac{4}{3}\mathrm{\pi }{r}^{3}=\frac{1}{3}\mathrm{\pi }×{\left(2.1\right)}^{2}×8.4\phantom{\rule{0ex}{0ex}}⇒{r}^{\mathit{3}}=\frac{2.1×2.1×8.4}{4}=2.1×2.1×2.1\phantom{\rule{0ex}{0ex}}⇒r=2.1\mathrm{cm}$

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