Question

A sphere has a surface area of 36π ft2. Find the volume of the sphere.

Answer 1

The surface area of the sphere is given by the equation

$A=4\pi * r^{2}$,

where A is the surface area and r is the radius.

We want to find the volume of the sphere, which is given by the equation

$V = \frac{4}{3} * \pi * r^{3}$,

where V is the volume and r is the radius.

Looking at these equations, we see that they both involve the sphere's radius. If we know what r is, we can calculate the volume.

We know that the sphere's surface area is $36 \pi$. Plugging that in for A in the surface area equation, we get

$36 \pi=4\pi * r^{2}$, then divide by $\pi$

$36 = 4 * r^{2}$, then divide by 4

$r^{2} = 9$, then take the square root of both sides

$r = 3$

So the radius of the sphere is 3. Plugging this into the volume equation,

$V = \frac{4}{3} * \pi * 3^{3}$, simplify terms

$V = \frac{4}{3} * \pi * 27$, multiply $\frac{4}{3}$ by 27

$V = 36 * \pi$

So the volume of the sphere is $36\pi$.

Answer 2

Answer:

36π ft^3

Step-by-step explanation:

The surface area (S) of a sphere can be defined as:

S = 4×π×r^2 = 36×π

Solve for r to get the radius of the sphere:

r = ($\sqrt{36/4}$ = 3

The voluem (V) of a sphere can be defined as:

V= (4/3)×π×r^3

The volume of the sphere is:

V = (4/3)×π×(3^3) = 36π ft^3

The volume of the sphere can be calculated from the surface area given.