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 ⠀⠀⠀⠀⠀⠀⠀

Question

asked Dec 15, 2023 114k views

1 Answer

Duncanp · Answer 1 · 2023-12-22T11:44:48+0000

Answer:

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:

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).