Question

If the total surface area of a solid hemisphere is $$462 \ cm^2$$, them find its volume.

Answer 1

Total surface area of a solid hemisphere $$= 462 cm^2$$
We know, Total surface area of a solid hemisphere $$= 3 \pi r^2$$
$$ 462 = 3 \pi r^2\\$$
$$r^2 = \dfrac{3234}{66}\\$$
or $$r = 7$$

Now, volume of solid hemisphere $$= \dfrac 2 3 \pi r^3$$
$$= \dfrac 23 \times \dfrac {22}7 \times 7 \times 7 \times 7 $$

$$ = \dfrac{2156}3\\$$
$$=718.67$$

So, volume of solid hemisphere is $$718.67 cm^3$$