A plane intersects the center of a sphere with a volume of about 113.1 m3. What is the area of the cross-section? Round to the nearest tenth.
area = m2
Let us find the radius of the sphere
113.1 = (4/3)pi r^3
113.1 / [ (4/3)pi ] = r^3 take the cube root
r ≈ 3 m
Then the area of the cross-section is just
pi * r^2 = pi (3)^2 = 9 pi ≈ 28.3 m^2