How can you express the area of a manhole in square feet from its diameter in inches?

To express the area of a manhole in square feet from its diameter in inches, the correct approach involves understanding the relationship between the diameter and the radius of a circle, as well as the conversion from square inches to square feet.

The area (A) of a circle can be calculated using the formula (A = \pi r^2), where (r) is the radius. Since the radius is half of the diameter, you can express the radius in terms of the diameter: (r = \frac{d}{2}). Substituting this into the area formula gives:

[ A = \pi \left(\frac{d}{2}\right)^2 = \pi \left(\frac{d^2}{4}\right) = \frac{\pi}{4} d^2 ]

This result shows that the area of the manhole can be expressed as (\frac{\pi}{4} d^2). The area is expressed in square inches when the diameter (d) is in inches.

Because there are 144 square inches in one square foot, if you needed to express the area in square feet, this result would require further conversion. However, the formula itself