How is the cross-section area of a 1-inch bolt calculated?

The cross-sectional area of a 1-inch bolt is calculated using the formula .7854 times the diameter squared. This formula derives from the area of a circle, which is computed as π multiplied by the radius squared (A = πr²). Since the diameter is twice the radius, we express the area in terms of diameter.

To transition from radius to diameter, we can express the radius as half of the diameter (r = d/2). Substituting this into the area formula gives A = π(d/2)², which simplifies to A = (π/4)d². The value of π/4 is approximately 0.7854, leading to the simplified formula for the area in terms of diameter: A = .7854 * d².

In the case of a 1-inch bolt, substituting the diameter (1 inch) into the formula will yield the area of the bolt's cross-section. This is crucial in engineering applications, as understanding the cross-sectional area aids in determining the strength and load-bearing capacity of the bolt in various mechanical systems.