What is the diameter of a circle with a cross-sectional area of 81 mils?

What is the diameter of a circle with a cross-sectional area of 81 mils?

• A. 7 mils
• B. 9 mils
• C. 11 mils
• D. 13 mils

Answer: (B)

To find the diameter of a circle given its cross-sectional area, one can use the formula for the area of a circle, which is \( A = \pi r^2 \), where \( A \) is the area and \( r \) is the radius. Since the problem states that the area is 81 mils², you can set up the equation: \[ 81 = \pi r^2 \] To solve for \( r^2 \), you can rearrange this to: \[ r^2 = \frac{81}{\pi} \] Next, take the square root of both sides to find \( r \): \[ r = \sqrt{\frac{81}{\pi}} \] Using the approximate value of \( \pi \) (around 3.14): \[ r \approx \sqrt{\frac{81}{3.14}} \approx \sqrt{25.8} \approx 5.08 \text{ mils} \] Since the diameter \( d \) is twice the radius, use the formula \( d = 2r \): \[ d \approx 2 \times 5.08 \approx 10.16 \text{ mils} \

To find the diameter of a circle given its cross-sectional area, one can use the formula for the area of a circle, which is ( A = \pi r^2 ), where ( A ) is the area and ( r ) is the radius. Since the problem states that the area is 81 mils², you can set up the equation:

[ 81 = \pi r^2 ]

To solve for ( r^2 ), you can rearrange this to:

[ r^2 = \frac{81}{\pi} ]

Next, take the square root of both sides to find ( r ):

[ r = \sqrt{\frac{81}{\pi}} ]

Using the approximate value of ( \pi ) (around 3.14):

[ r \approx \sqrt{\frac{81}{3.14}} \approx \sqrt{25.8} \approx 5.08 \text{ mils} ]

Since the diameter ( d ) is twice the radius, use the formula ( d = 2r ):

[ d \approx 2 \times 5.08 \approx 10.16 \text{ mils} \