The surface area of a sphere is 1017.4mm^2. What is the volume of the sphere? Use 3.14 for π and round to the nearest hundredth.
The formula for surface area of a sphere is:
SA = 4πr^2
where r is the radius of the sphere.
We can rearrange this formula to solve for the radius:
r = √(SA/4π)
Plugging in the given surface area and value of π:
r = √(1017.4/4(3.14))
r ≈ 8.03 mm
Now we can use the formula for volume of a sphere:
V = (4/3)πr^3
Plugging in the radius we just found:
V = (4/3)(3.14)(8.03)^3
V ≈ 2140.22 mm^3
Rounding to the nearest hundredth:
V ≈ 2140.22 mm^3 ≈ 2140.23 mm^3 (to the nearest hundredth)