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?
+658 \(\text{Cylinder volume formula}={\pi}r^2h=V\)
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.
