Question

The volume of a hemisphere is 19404 cm³. The total surface area of the hemisphere is
(a) 4158 cm²
(b) 16632 cm²
(c) 8316 cm²
(d) 3696 cm²

Answer 1

(a) 4158 cm²
Volume of hemisphere$=\frac{2}{3}\mathrm{\pi }{r}^3$
Therefore,

$$\begin{gathered} \frac{2}{3}\mathrm{\pi }{r}^3=19404 \\ \Rightarrow \frac{2}{3}\times \frac{22}{7}\times r^3=19404 \\ \Rightarrow r^3=\left(19404\times \frac{21}{44}\right) \\ \Rightarrow r^3={\left(21\right)}^3 \\ \Rightarrow r=21\text{cm} \end{gathered}$$

Hence, the total surface area of the hemisphere$=3\mathrm{\pi }{r}^2$
$$\begin{gathered} =\left(3\times \frac{22}{7}\times 21\times 21\right){\text{cm}}^2 \\ =4158{\text{cm}}^2 \end{gathered}$$