Formula of the Volume of a hemisphere:
V = [tex] \frac{2}{3} [/tex][tex] \pi [/tex]r³
144[tex] \pi [/tex] = [tex] \frac{2}{3} [/tex][tex] \pi [/tex]r³
Multiply by 3 to cancel fraction in the right side
144[tex] \pi [/tex] × 3 = 2[tex] \pi [/tex] r³
432 [tex] \pi [/tex] = 2[tex] \pi [/tex]r³
Divide by 2[tex] \pi [/tex] on either sides to isolate r³
[tex] \frac{432 \pi }{2 \pi } [/tex] = [tex] \frac{2 \pi }{2 \pi } [/tex]r³
2[tex] \pi [/tex] and [tex]2 \pi [/tex] cancel out
216 = r³
Take cube root to find the radius
[tex] \sqrt[3]{216} [/tex] = [tex] \sqrt[3]{r^3} [/tex]
6 = r
Radius is 6 units
The formula of the surface area of a hemisphere is:
S.A = 2[tex] \pi [/tex]r² + [tex] \pi [/tex]r²
= [tex] 2\pi [/tex](6)² + [tex] \pi [/tex](6)²
=2[tex] \pi [/tex] × 36 + 36[tex] \pi [/tex]
= 72[tex] \pi [/tex] + 36[tex] \pi [/tex]
= 108[tex] \pi [/tex] units² (in terms of [tex] \pi [/tex])
≈ 339.12 units²
Surface area = 108[tex] \pi [/tex] units
