A page measuring x by y is curved around to make an open cylinder with height y. Find the volume of the cylinder in terms of x and y.   Ans: `V=(x^2 y)/(4pi)`

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lemjay | High School Teacher | (Level 3) Senior Educator

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To determine the volume, apply the formula:

`V= pir^2h`

Since the height of the cylinder formed is y, plug-in h=y to the formula.


To determine the r, refer to the figure below. Notice that the side x in the rectangle is the perimeter of the base of the cylinder.

Since the base of a cylinder is a circle, apply the formula:


Then, plug-in P=x.


And divide both sides by 2pi.



Now that r is expressed in terms of x, plug-in this to V.






Hence, the volume of the cylinder formed is `V=(x^2y)/(4pi)` .

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