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)`
To determine the volume, apply the formula:
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)` .