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.

Did you find an error?

10. Five mark exercise problem II