QQuestionMathematics
QuestionMathematics
Find the diameter of a circle with an area of 12.6 square inches. Round your answer to the nearest hundredth.
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Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Recall the formula for the area of a circle
- $$\pi$$ is approximately 3.14159
The area of a circle is given by the formula: Where:
Step 3:: Rearrange the formula to solve for radius
r = \sqrt{\frac{A}{\pi}}
Step 4:: Substitute the given area
r = \sqrt{\frac{12.6}{\pi}}
Step 5:: Calculate the radius
r = \sqrt{\frac{12.6}{3.14159}} = \sqrt{4.0076} = 2.0025
Step 6:: Calculate the diameter
d = 2r = 2 \times 2.0025 = 4.005
The diameter is twice the radius:
Step 7:: Round to the nearest hundredth
d = 4.01
Final Answer
The diameter of the circle is 4.01 inches.
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