Answer:
3054 cm³
Step-by-step explanation:
You want the volume of a sphere that has the same radius and volume as a cylinder 12 cm high.
The volume formula for a sphere is ...
V = 4/3πr³
The volume formula for a cylinder is ...
V = πr²h
If the two volumes are the same and the radius is the same, then we have ...
4/3πr³ = πr²h
4/3r = h . . . . . . . . divide by πr²
r = 3/4h . . . . . . . . multiply by 3/4
If the cylinder is 12 cm high, the radii are ...
r = (3/4)(12 cm) = 9 cm
Then the volumes of the cylinder and sphere are ...
V = π(9 cm)²(12 cm) ≈ 3054 cm³
The volume of the sphere is about 3054 cm³.
