Q12. - Algebra 1

Question

Find the surface area of each solid.

Step-by-Step Solution

Answer

The surface area of the solid cylinder is 362.25 square centimeters.

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 5.1 cm and height 6.2 cm. Then, $r=5.1\mathrm{cm}$ and $h=6.2\mathrm{cm}$.

Step 3. Calculate the surface area.

Put $r=5.1$, $h=6.2$ and $\pi =\frac{22}{7}$ in $S=2\pi r\left(r+h\right)$ to get,

$$\begin{gathered} S=2\left(\frac{22}{7}\right)\left(5.1\right)\left(5.1+6.2\right) \\ =2\left(\frac{22}{7}\right)\left(5.1\right)\left(11.3\right) \\ \approx 362.25\left(\mathrm{roundedto}2\mathrm{decimalplaces}\right) \end{gathered}$$

So, $S\approx 362.25$.

Step 4. Determine the unit.

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

 

So, the surface area of the solid cylinder is approximately 362.25 square centimeters.