Question

If the surface area of a sphere is 144πm², then its volume (in m³ ) is
A. 288π
B. 316π
C. 300π
D. 188π

Answer 1

The required "option A) 288$\pi$ $m^{3}$" is correct.

Step-by-step explanation:

Given,

The surface area of a sphere =  144$\pi$ m²

Let r be the radius of sphere.

To find, the volume of a sphere (in $m^{3}$)  = ?

We know that,

The surface area of a sphere = 4$\pi$$r^{2}$

⇒ 4$\pi$$r^{2}$ = 144$\pi$

⇒ 4$r^{2}$ = 144

⇒ $r^{2}$ = 36 = $6^{2}$

⇒ r = 6 m

∴ The volume of a sphere = $\dfrac{4}{3} \pi r^3$

= $\dfrac{4}{3} \pi \times 6^3$

= $\dfrac{4}{3} \pi \times 216 m^{3}$

= 4$\pi$ × 72 $m^{3}$

= 288$\pi$ $m^{3}$

∴  The volume of a sphere = 288$\pi$ $m^{3}$

Thus, the required "option A) 288$\pi$ $m^{3}$" is correct.