Five mark exercise problem II — task. Mathematics State Board, Class 10.

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A solid sphere and a solid hemisphere have equal total surface area. Prove that the ratio of their volume is \(3 \sqrt{3}:4\).

Proof:

Let \(r_1\) be the radius of a sphere and \(r_2\) be the radius of a hemisphere.

\frac{π {r_{1}}^{2}}{π {r_{2}}^{2}} = \frac{i}{i}

\frac{r_{1}}{r_{2}} = \frac{\sqrt{i}}{i}

Ratio of their volumes \(=\)

\frac{(\frac{i}{i} π {r_{1}}^{i})}{(\frac{i}{i} π {r_{2}}^{i})}

\(=\)

\frac{i {r_{1}}^{i}}{{r_{2}}^{i}}

\(=\)

\frac{i \times {(\sqrt{i})}^{i}}{i^{i}}

\(=\)

\frac{i \sqrt{i}}{i}

Hence, proved.

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10. Five mark exercise problem II