Question

the figure below shows a circular courtyard.
its diameter is 84 m.

(a) use the calculator to find the area and circumference of the courtyard.
use 3.14 for π in your calculations, and do not round your answers.
make sure to include the correct units.

area:

circumference:

(b) the courtyard will be paved.
which measure would be used in finding the amount of pavement needed?

Explanation:

Part (a)

Area Calculation

Step1: Find the radius

The diameter \( d = 84 \, \text{m} \), so the radius \( r=\frac{d}{2}=\frac{84}{2} = 42 \, \text{m} \)

Step2: Use the area formula for a circle \( A=\pi r^{2} \)

Substitute \( \pi = 3.14 \) and \( r = 42 \) into the formula:
\( A=3.14\times42^{2} \)
First, calculate \( 42^{2}=42\times42 = 1764 \)
Then, \( A = 3.14\times1764=5538.96 \, \text{square meters} \)

Circumference Calculation

Step1: Use the circumference formula for a circle \( C=\pi d \)

Substitute \( \pi = 3.14 \) and \( d = 84 \) into the formula:
\( C = 3.14\times84=263.76 \, \text{meters} \)

Part (b)

To find the amount of pavement needed, we need to cover the surface of the courtyard. The area of a shape represents the amount of space it covers, while the circumference represents the length around it. So, the area is used to determine the amount of pavement.

Answer:

(a) Area: \( \boldsymbol{5538.96} \) square meters, Circumference: \( \boldsymbol{263.76} \) meters
(b) Area