Q19. - Algebra 1

Question

PUBLIC SAFETY The sound emitted from the siren of a tornado warning system can be heard for a 2.5 -mile radius. Find the area of the region that hears the siren. Round to the nearest tenth square mile.

Step-by-Step Solution

Answer

The area of the region that hears the siren is 19.6 square miles.

Step 1. State the formula.

The formula for the area of a circle is $A=\pi r^2$, where A is the area and r is the radius of the circle.

Step 2. List the given data.

The sound emitted from a siren of a tornado warning system can be heard for a 2.5 – mile radius. So, the radius of the region is 2.5 miles.

Step 3. Calculate the area.

Since sound is transmitted in all directions equally, this implies that the region that hears the siren is circular, with the siren being the center of the circular region.

Put $r=2.5$ and $\pi =\frac{22}{7}$ in $A=\pi r^2$ to get,

$$\begin{gathered} A=\frac{22}{7}{\left(2.5\right)}^2 \\ =6.25\left(\frac{22}{7}\right) \\ \approx 19.6429\left(\mathrm{roundedto}4\mathrm{decimalplaces}\right) \end{gathered}$$

So, $A\approx 19.6429$.

Step 4. Determine the unit.

Since the unit of the radius is given as miles, the unit of the area must be square miles. So, the area of the required region is approximately 19.6429 square miles.

Step 5. Rounding off.

Rounding off the area to the nearest tenth square mile, the area of the region that hears the siren is 19.6 square miles.