Question

I need help on number 10 urgently.

Answer 1

Answer: Option A. 288 cubic inches

Answer 2

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 !