Question

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

Answer 1

Answer:

The diameter of hemisphere is 9

Step-by-step explanation:

∵ the volume of the sphere is $\frac{4}{3}\pi r^{3}$

∴ The volume of the hemisphere is $\frac{2}{3}\pi r^{3}$

∵ 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

∴ $\frac{2}{3}\pi r^{3}=3\pi r^{2}$⇒divide both sides by πr²

∴ $\frac{2}{3}r=3$

∴ r =9/2

∴ The diameter of the hemisphere is 9