Which expression represents the volume of a cylinder using diameter D and length L?

Which expression represents the volume of a cylinder using diameter D and length L?

• A. V = D2 x .785 x D
• B. V = L x W x H
• C. V = Distance/time
• D. V = D2 x 746 x D

Answer: (A)

Volume of a cylinder is base area times height. The base is a circle with diameter D, so its radius is D/2. Area = π(D/2)^2 = (π/4) D^2. Multiply by the length L to get V = (π/4) D^2 L, which is about 0.785 D^2 L. So the expression with 0.785, D^2, and L matches the cylinder volume formula using diameter. The other options aren’t correct for a cylinder: one is for a rectangular prism, one is a rate (distance over time), and the last uses an unrelated constant.

Volume of a cylinder is base area times height. The base is a circle with diameter D, so its radius is D/2. Area = π(D/2)^2 = (π/4) D^2. Multiply by the length L to get V = (π/4) D^2 L, which is about 0.785 D^2 L. So the expression with 0.785, D^2, and L matches the cylinder volume formula using diameter. The other options aren’t correct for a cylinder: one is for a rectangular prism, one is a rate (distance over time), and the last uses an unrelated constant.