Question

Suppose the surface area of a sphere is 324π square units. What is the volume, in cubic units, of this sphere
A) 9π
B) 81π
C) 324π
D) 972π

Answer 1

D would be the answer

Answer 2

Answer:

Option D is correct

$972 \pi$ is the volume, in cubic units, of this sphere

Step-by-step explanation:

Surface area of sphere(S) and volume of sphere (V) is given by:

$S = 4 \pi r^2$

$V = \frac{4}{3} \pi r^3$                 .....[1]

As per the statement:

Suppose the surface area of a sphere is 324π square units

⇒S = 324π square units

then;

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

Divide both side by $4 \pi$ we have;

$81 = r^2$

or

$r^2= 81$

⇒$r = \sqrt{81} = 9$ units

We have to find  the volume, in cubic units, of this sphere.

Substitute the given value in [1] we have;

$V = \frac{4}{3} \pi \cdot 9^3 = \frac{4}{3} \pi \cdot 729$

Simplify:

$V = 4 \cdot \pi \cdot 243 = 972 \pi$ cubic units

Therefore, $972 \pi$ is the volume, in cubic units, of this sphere