What factor is multiplied by the diameter squared to find the volume of a right circular cylinder?

To find the volume of a right circular cylinder, the formula used is V = πr²h, where V is the volume, r is the radius, and h is the height of the cylinder. Since the radius is half of the diameter, we can express the radius in terms of the diameter (d) using the formula r = d/2.

Substituting this into the volume formula gives us:

V = π(d/2)²h
= π(d²/4)h
= (π/4) d²h

In this scenario, if we're looking to find the factor that is multiplied by the diameter squared in this formula, we arrive at π/4. The value of π is roughly 3.14, and when divided by 4, this results in approximately 0.785.

Therefore, the factor that is multiplied by the diameter squared to find the volume of a right circular cylinder is indeed 0.785. This aligns with the formula derived, where 0.785 represents π/4, thus confirming its role in the volume calculation of a cylinder based on its diameter squared and height.