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Question

# Find the surface area of a cube whose volume is (i) 343 m3 (ii) 216 dm3

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Solution

## $\left(\mathrm{i}\right)\phantom{\rule{0ex}{0ex}}\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{cube}=343{\mathrm{m}}^{3}\phantom{\rule{0ex}{0ex}}\mathrm{We}\mathrm{know}\mathrm{that}\mathrm{volume}\mathrm{of}\mathrm{a}\mathrm{cube}=\left(\mathrm{side}{\right)}^{3}\phantom{\rule{0ex}{0ex}}⇒\left(\mathrm{side}{\right)}^{3}=343\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.,\mathrm{side}=\sqrt[3]{343}=7\mathrm{m}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cube}=6×\left(\mathrm{side}{\right)}^{2}=6×\left(7{\right)}^{2}=294{\mathrm{m}}^{2}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{ii}\right)\phantom{\rule{0ex}{0ex}}\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{cube}=216{\mathrm{dm}}^{3}\phantom{\rule{0ex}{0ex}}\mathrm{We}\mathrm{know}\mathrm{that}\mathrm{volume}\mathrm{of}\mathrm{a}\mathrm{cube}=\left(\mathrm{side}{\right)}^{3}\phantom{\rule{0ex}{0ex}}⇒\left(\mathrm{side}{\right)}^{3}=216\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.,\mathrm{side}=\sqrt[3]{216}=6\mathrm{dm}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cube}=6×\left(\mathrm{side}{\right)}^{2}=6×\left(6{\right)}^{2}=216{\mathrm{dm}}^{2}$

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