Which formula gives the volume of a cylinder with base radius r and height h?

Which formula gives the volume of a cylinder with base radius r and height h?

• A. V = π r² h
• B. V = 2π r h
• C. V = π r h
• D. V = π r² / h

Answer: (A)

Volume is found by multiplying the base area by the height. For a cylinder, the base is a circle with area π r², so the total volume is π r² times h, giving V = π r² h. The other expressions mix in the side surface area or omit a factor of r, so they don’t measure the space the solid occupies. For example, 2π r h is the side surface area, not volume; π r h is missing a factor of r; and π r² / h would divide the volume by height, which isn’t correct.

Volume is found by multiplying the base area by the height. For a cylinder, the base is a circle with area π r², so the total volume is π r² times h, giving V = π r² h.

The other expressions mix in the side surface area or omit a factor of r, so they don’t measure the space the solid occupies. For example, 2π r h is the side surface area, not volume; π r h is missing a factor of r; and π r² / h would divide the volume by height, which isn’t correct.