Question

# A right circular cone is $5.4cm$ high and the radius of its base is $2cm$. It is melted and recast into another right circular one with a radius of base as $1.5cm$. find the height of the new cone formed.

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Solution

## The volume of the old cone = volume of the new cone $\frac{1}{3}\mathrm{\pi }×{{\mathrm{r}}_{1}}^{2}{\mathrm{h}}_{1}=\frac{1}{3}\mathrm{\pi }×{{\mathrm{r}}_{2}}^{2}{\mathrm{h}}_{2}\phantom{\rule{0ex}{0ex}}{{\mathrm{r}}_{1}}^{2}{\mathrm{h}}_{1}={{\mathrm{r}}_{2}}^{2}{\mathrm{h}}_{2}\phantom{\rule{0ex}{0ex}}{2}^{2}×5.4={\left(1.5\right)}^{2}×{\mathrm{h}}_{2}\phantom{\rule{0ex}{0ex}}{\mathrm{h}}_{2}=\frac{4×5.4}{2.25}\phantom{\rule{0ex}{0ex}}=\frac{21.6}{2.25}\phantom{\rule{0ex}{0ex}}{\mathrm{h}}_{2}=9.6\mathrm{cm}\phantom{\rule{0ex}{0ex}}$Therefore, the height of the new cone is $9.6cm$

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