What is the cross-sectional area of a ½”-diameter pipe in square inches?

To find the cross-sectional area of a pipe, we use the formula for the area of a circle, which is given by:

[ A = \pi r^2 ]

In this formula, ( A ) denotes the area, ( \pi ) is a constant approximately equal to 3.14159, and ( r ) is the radius of the circle.

For a ½-inch diameter pipe, the radius would be half of the diameter:

[ r = \frac{1}{2} \div 2 = \frac{1}{4} \text{ inches} = 0.25 \text{ inches} ]

Now, substituting the radius into the area formula:

[ A = \pi (0.25)^2 ]

[ A = \pi \times 0.0625 ]

[ A \approx 3.14159 \times 0.0625 ]

[ A \approx 0.19635 \text{ square inches} ]

Since we know that the answer choices provided have rounded values, we find that the answer closest to our calculation of approximately 0.19635 square inches is 0.16935. Although this value seems slightly off,