A rectangle with height 8 and length 24 is wrapped around a cylinder with height 8. The rectangle perfectly covers the curved surface of the cylinder without overlapping itself at all. What is the volume of the cylinder? My answer was wrong
+983 When the rectangle perfectly covers the curved surface of the cylinder without overlapping itself at all, the length of the rectangle forms a circle that the the base of the cylinder.
When we know the area of the base of the cylinder, we can multiply it by the height to find the volume.
Since the length of the rectangle is 24, the radius of the circle is \(\frac{12}{\pi}\).
The area is:
\((\frac{12}{\pi})^2\cdot\pi=\frac{144}{\pi}\)
The volume is \(144\cdot8\div\pi\)
I hope this helped,
Gavin
