A circle has an area of 64π in2. Which of the following is the circumference of the circle in terms of pi ( π)?
A.
9 π in
B.
16 π in
C.
4 π in
D.
8 π in
The Correct Answer and Explanation is:
To find the circumference of a circle given its area, we need to follow a series of steps involving the formulas for the area and circumference of a circle. Here’s a detailed explanation:
Step 1: Understand the given information. The area of the circle is given as 64π64\pi64π square inches. We need to find the circumference of the circle in terms of π\piπ.
Step 2: Use the formula for the area of a circle. The formula for the area AAA of a circle is: A=πr2A = \pi r^2A=πr2 where rrr is the radius of the circle.
We are given that: A=64πA = 64\piA=64π
Substitute 64π64\pi64π into the area formula: 64π=πr264\pi = \pi r^264π=πr2
Step 3: Solve for the radius rrr. To isolate r2r^2r2, divide both sides of the equation by π\piπ: 64=r264 = r^264=r2
Now, solve for rrr by taking the square root of both sides: r=64r = \sqrt{64}r=64 r=8 inchesr = 8 \text{ inches}r=8 inches
Step 4: Use the formula for the circumference of a circle. The formula for the circumference CCC of a circle is: C=2πrC = 2\pi rC=2πr
Substitute r=8r = 8r=8 inches into the circumference formula: C=2π×8C = 2\pi \times 8C=2π×8 C=16π inchesC = 16\pi \text{ inches}C=16π inches
Step 5: Review the options. The circumference of the circle is 16π16\pi16π inches, which corresponds to option B.
Conclusion: The correct answer is B. 16π16\pi16π inches.
Explanation Summary: To find the circumference from the area, first, determine the radius using the area formula. Then use the radius in the circumference formula. By calculating, we find the radius is 8 inches and thus the circumference is 16π16\pi16π inches. This step-by-step approach ensures accurate conversion from area to circumference.