Question

question 4 (multiple choice worth 1 points) kent has two similar cylindrical pipes, pipe a and pipe b. the radius of pipe a is 6 cm, and the radius of pipe b is 2 cm. what is the ratio of the volume of pipe a to the volume of pipe b? question 5 (multiple choice worth 1 points) a square has a side that measures 11 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.

Explanation:

Step1: Calculate square perimeter

\(P = 4s=4\times11 = 44\)

Step2: Find circle radius

\(r=\frac{C}{2\pi}=\frac{44}{2\times3.14}\approx7.01\)

Step3: Compute circle area

\(A=\pi r^{2}=3.14\times(7.01)^{2}\approx154.20\)

Answer:

1. First, find the perimeter of the square:

• The side - length of the square \(s = 11\) units. The perimeter of a square \(P\) is given by \(P=4s\).
• So, \(P = 4\times11=44\) units.

1. Then, find the radius of the circle:

• The circumference of a circle \(C = 2\pi r\), and we know that \(C = P=44\) units. Given \(\pi = 3.14\), we have \(44 = 2\times3.14\times r\).
• Solving for \(r\), we get \(r=\frac{44}{2\times3.14}=\frac{44}{6.28}\approx7.01\) units.

1. Finally, find the area of the circle:

• The area of a circle \(A=\pi r^{2}\). Substituting \(r\approx7.01\) and \(\pi = 3.14\), we have \(A = 3.14\times(7.01)^{2}\).
• \(A=3.14\times49.1401\approx154.20\) square units.