Question

(3)Find the volume of saup in a cylindrid con that13 Baches and 4 inches cross the lidFind the volume of a right cylunder whose heightso inches and whaşe bane has a circumference of1 echas gFind the volume of a cylinder whose base is aTrcle with e diameter of 18 Incher.

Answer 1

2) You have to find the volume of a right cylinder that has a height of 6 inches and a circumference of 16π inches.

The volume of a cylinder is equal to the product of the area of the circular base and the height of the shape, following the formula:

`V=\pi r^2\cdot h`

Before you can calculate the volume, you have to use the information about the circumference of the circle to determine the radius of the cylinder.

The circumference can be calculated as twice the product of the number pi and the radius of the circle, following the formula:

`C=2\pi r`

If you divide both sides of this formula by 2π you can use it to calculate the radius:

`\begin{gathered} (C)/(2\pi)=(2\pi r)/(2\pi) \\ r=(C)/(2\pi) \end{gathered}`

We know that C=16π, then the radius can be calculated as follows:

`\begin{gathered} r=(C)/(2\pi) \\ r=(16\pi)/(2\pi) \\ r=8in \end{gathered}`

The radius of the circle has a length of 8inches, now we can calculate the volume of the cylinder as follows:

r=8in

h=6in

`\begin{gathered} V=\pi r^2h \\ V=\pi\cdot(8^2)\cdot6 \\ V=\pi\cdot64\cdot6 \\ V=384\pi \end{gathered}`

The volume of the cylinder is 384π inches³