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

Answer:

3081.24 cm³ (nearest hundredth)

Step-by-step 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:

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

$\implies \sf r = \dfrac{44}{2 \pi}$

$\implies \sf r =\dfrac{22}{\pi}$

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

$\implies \sf V=\pi \left(\dfrac{22}{\pi}\right)^2(20)$

$\implies \sf V=\pi \left(\dfrac{484}{\pi^2}\right)(20)$

$\implies \sf V=\left(\dfrac{484}{\pi}\right)(20)$

$\implies \sf V=\dfrac{9680}{\pi}$

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

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