Q11. - Algebra 1

Question

Find the surface area of each solid.

Step-by-Step Solution

Answer

The surface area of the solid cylinder is 480.86 square inches.

Step 1. State the formula.

The formula for surface area of a solid cylinder is $S=2\pi r\left(r+h\right)$, where S is the surface area, 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 the given solid is a cylinder of radius 4.5 in. and height 12.5 in. Then, $r=4.5\mathrm{in}.$ and $h=12.5\mathrm{in}.$

Step 3. Calculate the surface area.

Put $r=4.5$, $h=12.5$ and $\pi =\frac{22}{7}$ in $S=2\pi r\left(r+h\right)$ to get,

$$\begin{gathered} S=2\left(\frac{22}{7}\right)\left(4.5\right)\left(4.5+12.5\right) \\ =2\left(\frac{22}{7}\right)\left(4.5\right)\left(17\right) \\ \approx 480.86\left(\mathrm{roundedto}2\mathrm{decimalplaces}\right) \end{gathered}$$

So, $S\approx 480.86$.

Step 4. Determine the unit.

Since the unit of radius and height are both given as inches, the unit of the surface area must be square inches.

 

So, the surface area of the solid cylinder is approximately 480.86 square inches.