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
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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.