Answer:
3081.24 cm³ (nearest hundredth)
Step-by-step explanation:
Formulas
[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
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:
[tex]\implies \sf 2 \pi r = 44[/tex]
[tex]\implies \sf r = \dfrac{44}{2 \pi}[/tex]
[tex]\implies \sf r =\dfrac{22}{\pi}[/tex]
Substitute the round radius into the formula for Volume and solve for V:
[tex]\implies \sf V=\pi \left(\dfrac{22}{\pi}\right)^2(20)[/tex]
[tex]\implies \sf V=\pi \left(\dfrac{484}{\pi^2}\right)(20)[/tex]
[tex]\implies \sf V=\left(\dfrac{484}{\pi}\right)(20)[/tex]
[tex]\implies \sf V=\dfrac{9680}{\pi}[/tex]
[tex]\implies \sf V=3081.239698...cm^3[/tex]
Therefore, the volume of the cylinder is 3081.24 cm³ (nearest hundredth).
