Question

A rectangular piece of paper is 44 cm long and 20 cm wide. A cylinder is forms by rolling the paper along its length. Find its volume

ASAP ⠀⠀⠀⠀⠀⠀⠀​

Answer 1

3081.24 cm³ (nearest hundredth)

Explanation:

Formulas

`\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}`

`\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}`

If a rectangular piece of paper is rolled along its length to form a cylinder:

• circumference = 44 cm
• height = 20 cm

To calculate the volume of the formed cylinder, determine the radius by using the circumference formula:

`\implies \sf 2 \pi r = 44`

`\implies \sf r = (44)/(2 \pi)`

`\implies \sf r =(22)/(\pi)`

Substitute the round radius into the formula for Volume and solve for V:

`\implies \sf V=\pi \left((22)/(\pi)\right)^2(20)`

`\implies \sf V=\pi \left((484)/(\pi^2)\right)(20)`

`\implies \sf V=\left((484)/(\pi)\right)(20)`

`\implies \sf V=(9680)/(\pi)`

`\implies \sf V=3081.239698...cm^3`

Therefore, the volume of the cylinder is 3081.24 cm³ (nearest hundredth).