Question

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 40.625pi

However, 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?

Answer 1

`\large\boxed{V\approx127.5625\ in^3}`

Explanation:

The formula of a volume of a cylinder:

`V=\pi r^2H`

r - radius

H - height

We have:

`2r=5\ in\to r=2(1)/(2)\ in\\\\H=6(1)/(2)\ in`

Convert the mixed numbers to the impropoer fractions:

`2(1)/(2)=(2\cdot2+1)/(2)=(5)/(2)\\\\6(1)/(2)=(6\cdot2+1)/(2)=(13)/(2)`

Substitute:

`V=\pi\left((5)/(2)\right)^2\left((13)/(2)\right)=\pi\left((25)/(4)\right)\left((13)/(2)\right)=(325)/(8)\pi\ in^3\\\\\pi\approx3.14\\\\V\approx(325)/(8)\cdot3.14=40.625\cdot3.14=127.5625\ in^3`