If the total surface area of a solid hemisphere is 462 cm2, find its volume. (Take π=227)

We are given total surface of hemisphere as

462 {cm}^{2}

.
Surface area of hemisphere is

3 π r^{2}

Where r = radius of hemisphere.
We know that surface area of hemisphere is,

3 π r^{2} = 462

\Rightarrow \frac{22}{7} r^{2} = \frac{462}{3}

\Rightarrow r^{2} = \frac{7}{22} \times \frac{462}{3}

\Rightarrow r^{2} = 49

\Rightarrow r = 7 cm

Now,
Volume of hemisphere is half the volume of sphere that is

\frac{2}{3} π r^{3}

\Rightarrow \frac{2}{3} π r^{3}

\Rightarrow \frac{2}{3} π {(7)}^{3}

\Rightarrow 718.67 {cm}^{3}

Thus, the volume of solid hemisphere is

718.67 {cm}^{3}

.
Therefore, the correct option is 2.

If the total surface area of a solid hemisphere is $462 {cm}^{2}$ , find its volume. (Take $π = \frac{22}{7}$ )