Question 95605: The volume of a can of soup is 144 PI inches cubed. The radius of the can is 6 inches. What is the height of the can? Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Given that the volume of a cylindrical can is:
. cubic inches
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and also given that the radius of the can is 6 inches.
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To find the height of the can you can begin by noting that the formula for finding the volume V
of a cylinder is based on multiplying the area A of the circular base of the cylinder times
the height H. In equation form this is:
.
.
and because A (the area of the circular base) can be found from the equation in
which R is the radius of the circle, we can substitute this value for A into the Volume formula
to get:
.
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The problem tells you that the value of R is 6 inches and the value of V is .
Substitute these values into the equation and you get:
.
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Since is a factor on both sides you can divide both sides by to cancel
the and reduce the equation to:
.
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Now recognize that . Substitute 36 into the equation and get:
.
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Solve for H by dividing both sides by 36 to get:
.
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and this divides out evenly to give you that:
.
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Since every dimension was in inches you know that the height H is 4 inches.
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Hope this helps you to understand the problem and a way that you can work it.
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