Q17. - Algebra 1

Question

Find the volume of each cylinder. Round to the nearest tenth.

Step-by-Step Solution

Answer

The volume of the given cylinder is 2772.0 cubic inches.

Step 1. State the formula.

The formula for volume me of a cylinder is $V=\pi r^{2}h$, where V is the volume, r is the radius and h is the height of the cylinder.

The formula for the radius of a cylinder is $r=\frac{d}{2}$, where d is the diameter of the cylinder.

Step 2. List the given data.

It is clear, from the given figure, that the diameter of the cylinder is 14 in. and the height of the cylinder is 18 in.

Then, $d=14\mathrm{in}.$ and $h=18\mathrm{in}.$

Step 3. Calculate the radius.

Put $d=14$ in $r=\frac{d}{2}$ to get,

$$\begin{gathered} r=\frac{14}{2} \\ =7 \end{gathered}$$

So, $r=7$.

Step 4. Calculate the volume.

Put $r=7$, $h=18$ and $\pi =\frac{22}{7}$ in $V=\pi r^{2}h$ to get,

$$\begin{gathered} V=\left(\frac{22}{7}\right){\left(7\right)}^2\left(18\right) \\ =22\times 7\times 18 \\ =2772 \end{gathered}$$

So, $V=2772$.

Step 5. Determine the unit.

Since the unit of both diameter and height of the cylinder is given as inches, the unit of volume must be cubic inches.

 

So, the volume of the cylinder is 2772 cubic inches.

Step 6. Rounding off.

Rounding to the nearest tenth, the volume of the given cylinder is 2772.0 cubic inches.