Question

The volume of a hemisphere is 144 pi. Find the radius and total surface area.

Answer 1

Formula of the Volume of a hemisphere:
V = $\frac{2}{3}$$\pi$r³
144$\pi$ = $\frac{2}{3}$$\pi$r³
Multiply by 3 to cancel fraction in the right side
144$\pi$ × 3 = 2$\pi$ r³
432 $\pi$ = 2$\pi$r³
Divide by 2$\pi$ on either sides to isolate r³
$\frac{432 \pi }{2 \pi }$ = $\frac{2 \pi }{2 \pi }$r³
2$\pi$ and $2 \pi$ cancel out
216 = r³
Take cube root to find the radius
$\sqrt[3]{216}$ = $\sqrt[3]{r^3}$
6 = r
Radius is 6 units

The formula of the surface area of a hemisphere is:
S.A = 2$\pi$r² + $\pi$r²
       = $2\pi$(6)² + $\pi$(6)²
       =2$\pi$ × 36 + 36$\pi$
       = 72$\pi$ + 36$\pi$
       = 108$\pi$ units²  (in terms of $\pi$)
       ≈ 339.12 units²

Surface area = 108$\pi$ units