A cylinder with a height of 6 1/2 inches. (In) and a diameter of 5 inches is shown.What is the volume of the cylinder, in cubic inches? (Use 3.14 for pi)The volume of the cylinder is 40.625piHowever, I’m doing work for why my answer is reasonable. So how do you do the math in order to get the cylinder to fit inside of a rectangular prism perfectly?

Accepted Solution

Answer:[tex]\large\boxed{V\approx127.5625\ in^3}[/tex]Step-by-step explanation:The formula of a volume of a cylinder:[tex]V=\pi r^2H[/tex]r - radiusH - heightWe have:[tex]2r=5\ in\to r=2\dfrac{1}{2}\ in\\\\H=6\dfrac{1}{2}\ in[/tex]Convert the mixed numbers to the impropoer fractions:[tex]2\dfrac{1}{2}=\dfrac{2\cdot2+1}{2}=\dfrac{5}{2}\\\\6\dfrac{1}{2}=\dfrac{6\cdot2+1}{2}=\dfrac{13}{2}[/tex]Substitute:[tex]V=\pi\left(\dfrac{5}{2}\right)^2\left(\dfrac{13}{2}\right)=\pi\left(\dfrac{25}{4}\right)\left(\dfrac{13}{2}\right)=\dfrac{325}{8}\pi\ in^3\\\\\pi\approx3.14\\\\V\approx\dfrac{325}{8}\cdot3.14=40.625\cdot3.14=127.5625\ in^3[/tex]