SOLUTION: Estimate the number of cubic inches of metal contained in a cylinder with a rectangular shaped opening in the middle if: the cylinder has a diameter of 14 inches and a height of 30

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Question 312049: Estimate the number of cubic inches of metal contained in a cylinder with a rectangular shaped opening in the middle if: the cylinder has a diameter of 14 inches and a height of 30 in. The rectangular hole is 7 inches by 7 inches with a height of 30 inches
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of the cylinder is
Vcyl=pi%2AR%5E2%2AH=pi%2A%2814%2F2%29%5E2%2A30=1470%2Api
The volume of the rectangular solid is
Vrs=l%2Aw%2Ah=7%2A7%2A30=1470
The volume of metal is the difference between the cylinder and solid volume,
Vm=Vcyl-Vrs=1470%2Api-1470=1470%2A%28pi-1%29 or approximately,
Vm=3148 cubic inches.