What is the formula for the cross-section of a 1-inch bolt?

The formula for the cross-sectional area of a circular object, such as a bolt, is derived from the area of a circle, which is given by the formula area = π × radius². However, since diameter is often used in practical applications, the formula can be rewritten in terms of diameter. The radius is half of the diameter (d/2), so when substituting this into the area formula, we have:

Area = π × (d/2)²

= π × (d²/4)

= (π/4) × d²

This value of (π/4) is approximately equal to 0.7854, which leads us to the formula:

Area = 0.7854 × diameter²

This is why the correct answer is the choice that expresses the cross-sectional area of a 1-inch bolt using the diameter. The other options do not fit the correct mathematical representation for the area of a circle and consequently would not yield the correct cross-sectional measurement needed for a bolt. The choice referring to diameter alone or multiplied by other coefficients does not correctly capture the circular area calculation needed in this context.