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
