A cylinder has a volume V. A second cylinder has twice the height and twice the radius. What is the volume of the second cylinder, in terms of V?

Guest Apr 5, 2020

edited by
Guest
Apr 5, 2020

#1**+2 **

\(\text{Cylinder volume formula}={\pi}r^2h=V\)

In other words, we are taking a circle and multipying it by the height of the cylinder.

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Since the second cylinder has twice the height and twice the radius, we plug that into the cylinder formula.

(1) \(\pi(2r)^22h={\pi}4r^22h\)

Since \({\pi}r^2h=V\), we divide by the cylinder formula to see how much V has changed.

1. \(\frac{{\pi}4r^22h}{{\pi}r^2h}=\frac{?}{V}\)

Canceling out, we get:

2. \(\frac{8}{1}=\frac{?}{V}\)

\(?=8V\)

The volume of the second cylinder is \(\boxed{8V}\)

Of course, you can always substitute real values, but its more fun for me to solve it algebraically.

AnExtremelyLongName Apr 5, 2020