Question

question 7 (multiple choice worth 1 points)
(05.01 mc)
a square has a side that measures 2.75 units. what is the area of a circle with a circumference that equals the perimeter of the square? use 3.14 for π, and round your answer to the nearest hundredth.
o 94.99 units²
o 23.75 units²
o 9.62 units²
o 38.47 units²

Explanation:

Step1: Calculate the perimeter of the square

The formula for the perimeter of a square is \(P = 4s\), where \(s\) is the side - length. Given \(s=2.75\) units, then \(P = 4\times2.75=11\) units. This perimeter is equal to the circumference of the circle, so \(C = 11\) units.

Step2: Find the radius of the circle

The formula for the circumference of a circle is \(C = 2\pi r\). We know \(C = 11\) and \(\pi = 3.14\). Rearranging for \(r\), we get \(r=\frac{C}{2\pi}\). Substituting the values: \(r=\frac{11}{2\times3.14}=\frac{11}{6.28}\approx1.75\) units.

Step3: Calculate the area of the circle

The formula for the area of a circle is \(A=\pi r^{2}\). Substituting \(r = 1.75\) and \(\pi=3.14\): \(A = 3.14\times(1.75)^{2}=3.14\times3.0625 = 9.61625\approx9.62\) units².

Answer:

9.62 units²