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Answer:
A cylinder 10 cm high with a circumference of 30 cm would have a greater volume
Step-by-step explanation:
Volume of a Cylinder
Given a cylinder of radius r and height h, the volume is calculated as:
[tex]V=\pi r^2h[/tex]
It's given a rectangular strip of aluminum 30 cm long and 10 cm wide. If we roll it to form a cylinder we can do it in two ways.
Rolling it across its length will make the cylinder have a height of h=10 cm and the circumference of the base equal to 30 cm.
The circumference of a circle of radius r is:
[tex]C=2\pi r[/tex]
Thus the radius is:
[tex]\displaystyle r=\frac{C}{2\pi}[/tex]
[tex]\displaystyle r=\frac{30}{2\pi}=\frac{15}{\pi}[/tex]
Thus the volume of the cylinder is:
[tex]V=\pi ( \frac{15}{\pi})^2*10[/tex]
[tex]V=\pi ( \frac{225}{\pi^2})*10[/tex]
[tex]V= \frac{2250}{\pi}[/tex]
If we rolled the strip across its width, then the height will be h=30 cm and the circumference C=10 cm, thus the radius is:
[tex]\displaystyle r=\frac{10}{2\pi}=\frac{5}{\pi}[/tex]
And the volume is:
[tex]V'=\pi ( \frac{5}{\pi})^2*30[/tex]
[tex]V'=\pi ( \frac{25}{\pi^2})*30[/tex]
[tex]V'= \frac{750}{\pi}[/tex]
Dividing V/V' = 3. The first volume it 3 times as much as the second volume.
A cylinder 10 cm high with a circumference of 30 cm would have a greater volume