Question

topic 7 mid - topic performance task mrs. velez has two rolls of garden edging that are each 96 inches long. she wants to make two new flower beds in her back yard. each flower bed will be bordered by one roll of the edging. one flower bed will be in the shape of a circle. the other will be in the shape of a quadrilateral. part a find the area of the circle that mrs. velez will border with one roll of edging. use 3.14 for π and round to the nearest hundredth. 7.gr.1.4

Explanation:

Step1: Find the circumference of the circle (edging length)

The length of the edging roll is the circumference \( C \) of the circle, so \( C = 96 \) inches. The formula for circumference of a circle is \( C = 2\pi r \), where \( \pi = 3.14 \). We solve for \( r \):
\( 96 = 2\times3.14\times r \)
\( 96 = 6.28r \)
\( r = \frac{96}{6.28} \approx 15.29 \) inches (rounded to two decimal places)

Step2: Calculate the area of the circle

The formula for the area of a circle is \( A = \pi r^2 \). Substitute \( \pi = 3.14 \) and \( r \approx 15.29 \):
\( A = 3.14\times(15.29)^2 \)
First, calculate \( (15.29)^2 \approx 233.78 \)
Then, \( A = 3.14\times233.78 \approx 734.07 \) square inches

Answer:

The area of the circle is approximately \(\boxed{734.07}\) square inches.