SOLUTION: A sphere will fit perfectly in a cube 6 in. on a side. What is the volume of the cube less that of the sphere. V= 4/3(3.14)r^3

Algebra ->  Volume -> SOLUTION: A sphere will fit perfectly in a cube 6 in. on a side. What is the volume of the cube less that of the sphere. V= 4/3(3.14)r^3      Log On


   

Question 624798: A sphere will fit perfectly in a cube 6 in. on a side. What is the volume of the cube less that of the sphere.
V= 4/3(3.14)r^3
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--

The Problem:
A sphere will fit perfectly in a cube 6 in. on a side. What is the volume of the cube less that of the 
sphere. Use the formula, V= 4/3(3.14)r^3, for the volume of the sphere.

Solution:
Since the sphere fits perfectly in the cube, its diameter is the same as the width of the cube, or 6 in. 
This translates to a radius of 3 in. since the radius is half the diameter.

Substitute 3 for r in the sphere volume formula.
V=%284%2F3%29%283.14%29r%5E3
V=%284%2F3%29%283.14%29%283%29%5E3
V=%284%2F3%29%283.14%29%2827%29
V=113.04

The volume of the sphere is 113.04 cubic inches.

Now we find the volume of the cube. The formula for the volume of a cube is V=s^3 where
s is the length of the cube's side. Substitute 6 for s in the formula.
V=s%5E3
V=6%5E3
V=216

The volume of the cube is 216 cubic inches,

To find the volume of the cube less the volume of the sphere, we subtract 216-113.04=102.96 cubic 
inches.

Please email me if you have questions or comments about the solution. I'm happy to explain further 
and I'd appreciate your feedback.

Ms.Figgy
math.in.the.vortex@gmail.com