a sphere has a volume of 500/3pi cubic centimeters. What is the total surface area, in square centimeters, of the sphere?

V = 4/3 π r^3

500/3π = 4/3 π r^3
500/4 = r^3
125 = r^3
r = 5

Now, Area = 4πr^2
...

To find the total surface area of a sphere, you can use the formula:

Surface Area = 4πr²

Where r is the radius of the sphere.
To find the radius, we can use the formula for the volume of a sphere:

Volume = (4/3)πr³

Given that the volume of the sphere is 500/3π cubic centimeters, we can equate it to the volume formula:

500/3π = (4/3)πr³

To solve for r, first, cancel out the π terms by multiplying both sides of the equation by (3/4)π:

r³ = (3/4) * (500/3π)
r³ = 500/(4π)

Next, take the cube root of both sides to find r:

r = (500/(4π))^(1/3)

Now that we have the radius, we can find the surface area using the formula mentioned earlier:

Surface Area = 4πr²
Surface Area = 4π * [(500/(4π))^(1/3)]²

Simplifying this expression would give you the total surface area of the sphere in square centimeters.