Question

If the area of a circle is 75.7ft2, what is the radius? Give the answer in metres. Round answer to 2 decimal places and enter the units.

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Maude

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81 Answers

To find the radius (\(r\)) of a circle when given the area (\(A\)), you can use the formula:
\[ A = \pi r^2 \]
Given that the area of the circle is \(75.7 \, \text{ft}^2\) , you can set up the equation:
\[ 75.7 = \pi r^2 \]
To find \(r\) , divide both sides by \(\pi\) :
\[ r^2 = \frac{75.7}{\pi} \]
Now, take the square root of both sides:
\[ r = \sqrt{\frac{75.7}{\pi}} \]
Using a calculator to get the numerical value:
\[ r \approx \sqrt{\frac{75.7}{3.14159}} \]
\[ r \approx \sqrt{24.11} \]
\[ r \approx 4.91 \]
So, the radius is approximately 4.91 feet. Now, you want to convert this to meters. Since 1 foot is approximately 0.3048 meters:
\[ r \approx 4.91 \, \text{ft} \times 0.3048 \, \text{m/ft} \]
\[ r \approx 1.4967 \, \text{m} \]
Therefore, the radius is approximately 1.50 meters (rounded to 2 decimal places).

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