Asphere has a surface area of 36π ft2. find the volume of the sphere.

36π ft3

42π ft3

48π ft3

28π ft3

The surface area of the sphere is given by the equation

,

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

,

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 . Plugging that in for A in the surface area equation, we get

, then divide by

, then divide by 4

, then take the square root of both sides

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

, simplify terms

, multiply by 27

So the volume of the sphere is .

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 = ( = 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.