Question

3 formula 0.5 points a 85.5-inch strip of metal is bent into a circular hoop. a straight line is drawn from one side of the hoop to the other, passing through the center. what is the length of that line? use 3.14 for pi. round your answer to the nearest hundredth of an inch, but do not include \in\ with your response. answer 4 formula 0.5 points what is the area of a circle with a radius of 12.1 ft? use 3.14 for pi. round your answer to the nearest hundredth of a foot, but do not include \ft\ with your response. answer

Explanation:

Question 3

Step1: Find the circumference formula

The length of the metal strip is the circumference \( C \) of the circle, and \( C = \pi d \), where \( d \) is the diameter (the length of the straight line through the center). First, recall \( C = 85.5 \) inches and \( \pi = 3.14 \).

Step2: Solve for diameter \( d \)

From \( C = \pi d \), we can rearrange to \( d=\frac{C}{\pi} \). Substitute \( C = 85.5 \) and \( \pi = 3.14 \): \( d=\frac{85.5}{3.14} \approx 27.23 \).

Step1: Recall the area formula of a circle

The area \( A \) of a circle is given by \( A=\pi r^{2} \), where \( r = 12.1 \) ft and \( \pi = 3.14 \).

Step2: Calculate \( r^{2} \)

First, find \( r^{2}=(12.1)^{2}=146.41 \).

Step3: Calculate the area

Multiply by \( \pi \): \( A = 3.14\times146.41 \approx 459.73 \).

Answer:

27.23

Question 4