Question

The volume of a solid hemisphere is `396/7` cm³. The total surface area of the solid hemisphere (in sq. cm) is ______.

Options

• `396/7`

• `594/7`

• `549/7`

• `604/7`

Answer 1

The volume of a solid hemisphere is `396/7` cm³. The total surface area of the solid hemisphere (in sq. cm) is `underlinebb(594/7)`.

Explanation:

Given,

The volume of a solid hemisphere is `396/7` cm³.

The volume of solid hemisphere = `2/3pir^3`

`396/7  cm^3 = 2/3 xx 22/7 xx r^3`

`396/7 xx 3/2 xx 7/22  cm^3` = r³

∴ r = `root3(3 xx 3xx 3  cm^3)` = 3 cm

∴ The total surface area of the hemisphere = 3πr²

= `3 xx 22/7 xx (3  cm) ^2`

= `(3 xx 22 xx 9)/7  cm^2`

= `594/7` cm²