Question

If the surface area of a sphere is (144π) m², then its volume is
(a) (288π) m³
(b) (188π) m³
(c) (300π) m³
(d) (316π) m³

Answer 1

(a) (288π) m³

Surface area = (144π) m²
Ler r m be the radius of the sphere.
Then we have:

$$\begin{gathered} 4\mathrm{\pi }{r}^2=144\mathrm{\pi } \\ \Rightarrow r^2=\frac{144}{4}=36 \\ \Rightarrow r=6\mathrm{m} \\ \therefore \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{sphere}=\frac{4}{3}\mathrm{\pi }{r}^3 \\ =\frac{4}{3}\mathrm{\pi }\times 6\times 6\times 6 \\ =288\mathrm{\pi }{\mathrm{m}}^3 \end{gathered}$$