mistyped before. A sphere has a volume of 500/3 pi cubic centimeters. What is the total surface area in square centimeters, of the sphere? The correct answer is 100pi, but I have no idea why. I need to see it worked out from start to finish :(

Just realized that bobpursley had answered your question before you posted it for the third time.

Please check to see if your questions are answered before you post it again.
http://www.jiskha.com/display.cgi?id=1318643925

To find the total surface area of a sphere, we need to know its volume. However, you provided the volume of the sphere. So, let's first use the volume of the sphere to find its radius.

The formula for the volume of a sphere is given by:

V = (4/3) * π * r^3

Given that the volume is (500/3) * π, we can set up the equation as:

(500/3) * π = (4/3) * π * r^3

We can cancel out the π terms from both sides of the equation:

500/3 = (4/3) * r^3

Now, let's solve for r^3 by dividing both sides of the equation by (4/3):

(500/3) / (4/3) = r^3

Simplifying the equation, we get:

500 / 4 = r^3

125 = r^3

Now, to find the value of r, we take the cube root of both sides:

∛125 = ∛r^3

5 = r

So, the radius of the sphere is 5 cm. Now, let's calculate the total surface area of the sphere.

The formula for the surface area of a sphere is given by:

A = 4 * π * r^2

Substituting the value of r, we get:

A = 4 * π * 5^2

A = 4 * π * 25

A = 100 * π

Therefore, the total surface area of the sphere is 100π square centimeters.

To find the surface area of a sphere, you'll need to use the formula:

Surface Area = 4πr^2

But first, we need to find the radius (r) of the sphere.

The volume of a sphere is given by the formula:

Volume = (4/3)πr^3

Given that the volume of the sphere is 500/3π cubic centimeters, we can set up the equation as follows:

500/3π = (4/3)πr^3

To simplify the equation, we can cancel out π on both sides:

500/3 = (4/3)r^3

Next, we can solve for r^3 by multiplying both sides by 3/4:

(3/4)(500/3) = r^3

Simplifying that equation gives:

r^3 = 125

Taking the cubic root of both sides gives us the radius:

r = 5

Now that we have the radius, we can substitute it into the surface area formula:

Surface Area = 4πr^2
= 4π(5^2)
= 4π(25)
= 100π

Therefore, the total surface area of the sphere is 100π square centimeters.

V = (4/3)πr^3

(500/3)π = (4/3)πr^3
r^3 = 125
r = 5

Surface area of sphere = 4πr^2
= 4π(5^2) = 100π