Question

If the surface area of a sphere is $324\pi c{m}^2$ then its volume is

• A. $950\pi c{m}^3$
• B. $972\pi c{m}^3$
• C. $975\pi c{m}^3$
• D. $980\pi c{m}^3$

Answer 1

Answer: (B)

$972\pi c{m}^3$

Consider the given surface area of sphere $=324\pi c{m}^3$

Let, radius of sphere =r

We know that,

Surface area of the sphere$=4\pi r^{2}c{m}^3$

Now,

$4\pi r^2=324\pi$

$r^2=81$

$r=9cm$

$\frac{4}{3}\pi r^3=4851$

$r^3=\frac{3\times 4851\times 7}{4\times 22}$

Now, volume of the sphere,

$=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\pi \times 9^{3}c{m}^3$

$=972\pi c{m}^3$

Hence, this is the answer.