Question

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere?

Answer 1

The diameter of hemisphere is 9

Explanation:

∵ the volume of the sphere is
`(4)/(3)\pi r^(3)`

∴ The volume of the hemisphere is
`(2)/(3)\pi r^(3)`

∵ The surface area of the hemisphere is
`2\pi r^(2)+\pi r^(2)`

∴ The surface area of the hemisphere
`3\pi r^(2)`

∵ The volume of the hemisphere = the surface area of it

∴
`(2)/(3)\pi r^(3)=3\pi r^(2)`⇒divide both sides by πr²

∴
`(2)/(3)r=3`

∴ r =9/2

∴ The diameter of the hemisphere is 9