Question

find the circumference of each circle. 23) area = 64π mi². 16π mi. find the area of each. 25) circumference = 6π yd. 9π yd². 24) area = 16π yd². 8π yd. 26) circumference = 22π m. 121π m²

Explanation:

1. Problem 23: Given area \(A = 64\pi\) square - inches, find the circumference \(C\)

• Step 1: Find the radius \(r\) using the area formula
• The area formula of a circle is \(A=\pi r^{2}\). Given \(A = 64\pi\), we have \(\pi r^{2}=64\pi\). Divide both sides by \(\pi\): \(r^{2}=64\), so \(r = 8\) inches (since \(r>0\)).
• Step 2: Calculate the circumference using the radius
• The circumference formula of a circle is \(C = 2\pi r\). Substitute \(r = 8\) into the formula: \(C=2\pi\times8=16\pi\) inches.

1. Problem 24: Given area \(A = 16\pi\) square - feet, find the circumference \(C\)

• Step 1: Find the radius \(r\) using the area formula
• Since \(A=\pi r^{2}\) and \(A = 16\pi\), divide both sides by \(\pi\): \(r^{2}=16\), so \(r = 4\) feet (since \(r>0\)).
• Step 2: Calculate the circumference using the radius
• Using \(C = 2\pi r\), substitute \(r = 4\) into the formula: \(C=2\pi\times4 = 8\pi\) feet.

1. Problem 25: Given circumference \(C = 6\pi\) yards, find the area \(A\)

• Step 1: Find the radius \(r\) using the circumference formula
• The circumference formula is \(C = 2\pi r\). Given \(C = 6\pi\), we have \(2\pi r=6\pi\). Divide both sides by \(2\pi\): \(r = 3\) yards.
• Step 2: Calculate the area using the radius
• The area formula is \(A=\pi r^{2}\). Substitute \(r = 3\) into the formula: \(A=\pi\times3^{2}=9\pi\) square - yards.

1. Problem 26: Given circumference \(C = 22\pi\) meters, find the area \(A\)

• Step 1: Find the radius \(r\) using the circumference formula
• Since \(C = 2\pi r\) and \(C = 22\pi\), divide both sides by \(2\pi\): \(r = 11\) meters.
• Step 2: Calculate the area using the radius
• Using \(A=\pi r^{2}\), substitute \(r = 11\) into the formula: \(A=\pi\times11^{2}=121\pi\) square - meters.

Answer:

1. \(16\pi\) inches
2. \(8\pi\) feet
3. \(9\pi\) square - yards
4. \(121\pi\) square - meters