The volume of a sphere is 5000 π m3. What is the lateral surface area of the sphere to the nearest square meter?
We can use the formula for the volume of a sphere:
V = (4/3)πr^3
where r is the radius of the sphere. Rearranging the formula, we get:
r^3 = (3V)/(4π)
We can then solve for r:
r = [(3V)/(4π)]^(1/3)
Plugging in V = 5000π, we get:
r = [(3 × 5000π)/(4π)]^(1/3) ≈ 16.08 m
The lateral surface area of the sphere is given by:
A = 4πr^2
Plugging in r ≈ 16.08, we get:
A ≈ 3233.95 m^2
Rounding to the nearest square meter, the lateral surface area is:
A ≈ 3234 m^2
To find the lateral surface area of a sphere, we first need to find the radius of the sphere using the volume given.
The volume of a sphere is given by the formula:
V = 4/3 * π * r^3
We can rearrange this formula to solve for the radius:
r^3 = V * 3 / (4 * π)
r = (V * 3 / (4 * π))^(1/3)
Substituting the given volume of 5000 π m^3:
r = (5000 π * 3 / (4 * π))^(1/3)
r = (15000 / 4)^(1/3)
r = 25^(1/3)
r ≈ 2.924 m
Now that we have the radius, we can calculate the lateral surface area of the sphere using the formula:
A = 4 * π * r^2
Substituting the radius we just found:
A = 4 * π * (2.924)^2
A ≈ 107.22 m^2
Therefore, the lateral surface area of the sphere is approximately 107 square meters.