Geometry word problem, help please.

Question

A 6 inch diameter sphere is pressed into half of its size as it is pushed down into a 9 inch cylinder with a diameter of 6 inches. How much space is left in the cylinder?

 

A. 141.3 cubic inches

B. 197.82 cubic inches

C. 235.5 cubic inches

D. 904.32 cubic inches

Answer 1

It's not entirely clear what the question is asking, but I'll assume it means the 6 inch sphere loses half its volume when pressed into the cylinder.

 

Find the volume of the cylinder:

 

V_c = πr²h

V_c = π(3)²(9)

V_c = 9π(9)

V_c = 81π in³

 

Find the volume of the sphere, then divide by 2:

 

V_s = 4/3πr³

V_s = 4/3π(3)³

V_s = 4/3π(27)

V_s = 108/3π

V_s = 36π in³

 

V_s/2 = (36π)/2 = 18π in³

 

Subtract half the volume of the sphere from the volume of the cylinder to find out how much space is left:

 

V_c - V_s/2 = 81π - 18π = 63π ≈ 197.92 in³

 

This is close to answer B.