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

Using the total surface area formula for a solid hemisphere, 3 * pi * r^2 = 462, we find the radius by calculating r^2 = 462 * 7 / 66, which gives r = 7 cm. The volume of a solid hemisphere is (2/3) * pi * r^3, so substituting the values gives (2/3) * (22/7) * 7^3 = 718.67 cm^3.

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