Given:
A circle with an area of 225π square feet.
We need to determine the volume and surface area of a sphere derived from this circle.
A = πr^2
solve for r:
225π = πr^2
225 = r^2
r = 15 feet
Volume of a sphere:
V = 4/3 π r^3
V = 4/3 π (15)^3
V = 4500π cubic feet
The surface area of a sphere:
SA = 4πr^2
SA = 4π * (15^2)
SA = 900π square feet.
Therefore the answer of this problem is letter A:
A) A: V = 4500π ft3; S = 900π ft2