The volume of a sphere is 4,000 m3. What is the surface area of the sphere to the nearest square meter?
A. 2614 m2
owo
Why did the sphere roll down the hill? Because it wanted to calculate its surface area!
But seriously, let's calculate it. To find the surface area of a sphere, we can use the formula A = 4πr^2, where A is the surface area and r is the radius of the sphere.
First, let's find the radius. We know that the volume of the sphere is 4,000 m^3, so we can use the formula V = (4/3)πr^3. Rearranging this formula, we get r = (3V / 4π)^(1/3).
Plugging in the value for V, we get r = (3 * 4000 / (4 * π))^(1/3), which simplifies to r = (3000 / π)^(1/3).
Now, we can plug this value back into the formula for the surface area A = 4πr^2.
A = 4 * π * ((3000 / π)^(1/3))^2
Calculating this, we find that the surface area of the sphere is approximately 120,573 square meters. So, to the nearest square meter, the surface area of the sphere is 120,573 square meters.
To find the surface area of a sphere, you need to know its radius. However, in this case, we are only given the volume of the sphere. To find the radius, we can use the formula for the volume of a sphere.
The formula for the volume of a sphere is:
V = (4/3) * π * r^3
Given that the volume V is 4,000 m^3, we can rearrange the formula to solve for r:
4,000 = (4/3) * π * r^3
Dividing both sides of the equation by (4/3) * π gives:
4,000 / [(4/3) * π] = r^3
Rearranging further to solve for r:
r^3 = (3/4) * 4,000 / π
Taking the cube root of both sides gives:
r = [(3/4) * 4,000 / π]^(1/3)
Now that we have the value of the radius (r), we can calculate the surface area of the sphere using the formula:
A = 4 * π * r^2
Substituting the value of r into the formula, we get:
A = 4 * π * [(3/4) * 4,000 / π]^(1/3)^2
Simplifying further:
A = 4 * π * [(3/4) * 4,000 / π]^(2/3)
Calculating this expression will give you the surface area of the sphere.
ffv
V = (4/3)πr^3
SA = 4πr^2
(4/3)π r^3 = 4000
r^3 = 3000/π
r = (3000/π)^(1/3)
SA = 4π(3000/π)^(2/3) = appr 1219 m^2