Question

if the total surface area of a hemisphere is 462 cmsq find its volume

Answer 1

Total surface area of hemisphere = 3πr² = 462 cm²
Taking π as 22/7
 3*22/7 * r² = 462
r² = 462*7 / 66
r² = 49
r = 7 cm

The volume of hemisphere = 2/3πr³  = 2/3*22/7*(7)³
                                                              = 2/3 * 22/7 * 343
                                                              = 718.66667 cm³

Answer 2

Let the radius of hemisphere be "r"
Therefore, According to question,



$3\pi {r}^{2} = 462 \\ \pi {r}^{2} = 154 \\ {r}^{2} = 154 \times \frac{7}{22} \\ {r}^{2} = 49 \\ r = 7$


Therefore, volume of Hemisphere =

$\frac{2}{3} \pi {r}^{3} \\ = \frac{2}{3} \times \frac{22}{7} \times 7 \times 7 \times 7 \\ = 718.66 \: {cm}^{3} \: (approx.)$