SOLUTION: Three identical spheres of radius 4 inches, are placed in a cylinder of radius 7 inches. Find the minimum volume of water needed to completely submerge the three spheres.

Algebra ->  Volume -> SOLUTION: Three identical spheres of radius 4 inches, are placed in a cylinder of radius 7 inches. Find the minimum volume of water needed to completely submerge the three spheres.      Log On


   



Question 1025614: Three identical spheres of radius 4 inches, are placed in a cylinder of radius 7 inches. Find the minimum volume of water needed to completely submerge the three spheres.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Three identical spheres of radius 4 inches, are placed in a cylinder of radius 7 inches. Find the minimum volume of water needed to completely submerge the three spheres.
===================
Make a sketch with 4" circles inside a rectangle 14" wide.
The bottom sphere is tangent to the bottom and 1 side.
The middle sphere is tangent to the other side and the bottom sphere.
Its center is 4 + sqrt(28) from the bottom.
The top sphere's center is at 4 + 2sqrt(28) from the bottom --> the top of the top sphere is 8 + 2sqrt(28) inches from the bottom.
---------
Vol of the cylinder is pi%2Ar%2A2%2Ah
Subtract 3 times one sphere's volume:
--> pi%2A49%2A%288%2B2sqrt%2828%29%29+-+3%2A4%2Api%2A64%2F3
= pi%2A49%2A%288%2B2sqrt%2828%29%29+-+256pi cubic inches
=~ 460.5 cu in