Q20. - Algebra 1

Question

HISTORY Stonehenge is an ancient monument in Wiltshire, England. The giant stones of Stonehenge are arranged in a circle 30 meters in diameter. Find the area of the circle. Round to the nearest tenth square meter.

Step-by-Step Solution

Answer

The area of the circle is 707.1 square meters.

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

Step 2. List the given data.

The stones of Stonehenge are arranged in a circle 30 meters in diameter. So, the diameter of the circle is 30 meters.

Step 3. Calculate the radius.

Put $d=30$ in $r=\frac{d}{2}$ to get,

$\begin{array}{c}r=\frac{30}{2}\\ =15\end{array}$

So, $r=15$.

Step 4. Calculate the area.

Put $r=15$ and $\pi =\frac{22}{7}$ in $A=\pi r^2$ to get,

$$\begin{gathered} A=\frac{22}{7}{\left(15\right)}^2 \\ =\frac{22}{7}\left(225\right) \\ \approx 707.1429\left(\mathrm{Roundedto}4\mathrm{decimalplaces}\right) \end{gathered}$$

So, $A\approx 707.1429$.

Step 5. Determine the unit.

Since, the unit of diameter is given as meters, the unit of the radius obtained is also metered and thus the unit of the obtained area is square meters. So, the required area is 707.1429 square meters.

Step 6. Rounding off.

Rounding off the obtained area to the nearest tenth square meter, the area of the circle is 707.1 square meters.