Questions: Find the area of the circle with the given radius. r=45.7 yd The area is □ yd^2 (Type your answer using the appropriate number of significant digits.)

Find the area of the circle with the given radius.
r=45.7 yd

The area is □ yd^2
(Type your answer using the appropriate number of significant digits.)

Transcript text: Find the area of the circle with the given radius. \[ \mathrm{r}=45.7 \mathrm{yd} \] The area is $\square$ $y d^{2}$ (Type your answer using the appropriate number of significant digits.)

Solution

Solution Steps

Step 1: Given Information

The radius of the circle is given as $ r = 45.7 \, \text{yd} $.

Step 2: Area Formula

To find the area $ A $ of the circle, we use the formula: \[ A = \pi r^2 \]

Step 3: Calculate the Area

Substituting the value of the radius into the formula: \[ A = \pi (45.7)^2 \] Calculating $ (45.7)^2 $: \[ (45.7)^2 = 2088.49 \] Thus, the area becomes: \[ A = \pi \times 2088.49 \approx 6561.184841095748 \]

Step 4: Significant Digits

The radius $ 45.7 $ has 3 significant digits. Therefore, we round the area to 3 significant digits: \[ A \approx 6.56 \times 10^3 \, \text{yd}^2 \]