Q16. - 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 5707.0 cubic centimeters.

Step 1. State the formula.

The formula for the volume 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.

Step 2. List the given data.

It is clear, from the given figure, that both the radius and the height of the cylinder is 12.2 cm.

Then, $r=12.2\mathrm{cm}$ and $h=12.2\mathrm{cm}$.

Step 3. Calculate the volume.

Put $r=12.2$, $h=12.2$ and $\pi =\frac{22}{7}$ in $V=\pi r^{2}h$ to get,

$$\begin{gathered} V=\left(\frac{22}{7}\right){\left(12.2\right)}^2\left(12.2\right) \\ =\left(\frac{22}{7}\right){\left(12.2\right)}^3 \\ =\left(\frac{22}{7}\right)\left(1815.848\right) \\ \approx 5706.9509\left(\mathrm{roundedto}4\mathrm{decimalplaces}\right) \end{gathered}$$

So, $V\approx 5706.9509$.

Step 4. Determine the unit.

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

 

So, the volume of the cylinder is approximately 5706.9509 cubic centimeters.

Step 5. Rounding off.

Rounding to the nearest tenth, the volume of the given cylinder is 5707.0 cubic centimeters.