Question

If the surface area of sphere is $\left(144\pi \right)m^2$, then its volume is

• A. $\left(288\pi \right)m^3$
• B. $\left(188\pi \right)m^3$
• C. $\left(300\pi \right)m^3$
• D. $\left(316\pi \right)m^3$

Answer 1

The correct option is A $\left(288\pi \right)m^3$

Surface area of sphere $=4\pi r^2$

$\Rightarrow 4\pi r^2=144\pi$

$\Rightarrow r=\sqrt{\frac{144}{4}}=\sqrt{{\left(\frac{12}{2}\right)}^2}=6m$

$\Rightarrow$ Volume $=\frac{4}{3}\pi r^3=\frac{4}{3}\times \pi \times 6^3=288\pi m^3.$

Hence, the answer is $\left(288\pi \right)m^3.$