The volume of a sphere is 750 m3. What is the surface area of the sphere?
The formula for the volume of a sphere is given by V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.
We are given that the volume of the sphere is 750 m^3, so we can set up the equation as follows:
750 = (4/3)πr^3
To find the radius, we need to isolate r in the equation.
Dividing both sides of the equation by (4/3)π, we get:
r^3 = (750 * 3) / (4π)
r^3 = 2250 / (4π)
Taking the cube root of both sides of the equation, we have:
r = (2250 / (4π))^(1/3)
Now that we have the radius, we can use the formula for the surface area of a sphere, which is given by S = 4πr^2, where S is the surface area and r is the radius of the sphere.
Plugging in the value of r, we have:
S = 4π((2250 / (4π))^(1/3))^2
Simplifying the expression, we have:
S = 4π(2250 / (4π))^(2/3)
S = 4π(2250^(2/3) / (4π)^(2/3))
Simplifying further, we have:
S = 4π(2250^(2/3) / 4^(2/3) * π^(2/3))
S = 4π(2250^(2/3) / 2 * π^(2/3))
S = 2(2250^(2/3) / π^(1/3))
Therefore, the surface area of the sphere is 2(2250^(2/3) / π^(1/3)) square meters.