The formula for the volume of a cylinder is
V = π · R² · Height .
The formula for the volume of a sphere is
V = 4/3 · π · R³ .
We know the volume of the cylinder, so let's work with that formula, and see if we can squeeze anything out of it that can help us with the sphere.
Cylinder: V = π · R² · Height .
Wow ! Look at the picture for a second ! The radius of the cylinder is the same as the radius of the sphere, AND the height of the cylinder is double the radius ! This should really help.
Cylinder: V = π · R² · (2R) .
V = π · (2R³)
But we know the volume of the cylinder. It's 432π inch³ .
432π in³ = π · 2R³
Divide each side by 2 :
π R³ = 216 in³
We could use this to find the radius, but why bother ? Why not just keep (π R³) and stuff it straight into the formula for the volume of the sphere ! ?
Sphere: V = 4/3 · (π · R³)
V = 4/3 · (216 in³)
V = (4/3 · 216) in³
V = 288 in³
Ahhh ... the sweet feeling of knowing that you're right !