What is the formula for the volume of a cylinder?

What is the formula for the volume of a cylinder?

• A. V = πr²h
• B. V = 2πrh
• C. V = πd²h/4
• D. V = r h

Answer: (A)

Volume is found by base area times height. A cylinder has a circular base, whose area is πr^2, so multiplying by the height h gives V = πr^2h. This is the standard form because it directly uses the radius of the circular base. If you prefer to express the answer with the diameter d, use r = d/2 and get V = π(d/2)^2h = (πd^2h)/4, which matches another common form. The other expressions don’t represent volume: 2πrh is the lateral surface area, and r h misses the necessary factors to cover the circular base.

Volume is found by base area times height. A cylinder has a circular base, whose area is πr^2, so multiplying by the height h gives V = πr^2h. This is the standard form because it directly uses the radius of the circular base. If you prefer to express the answer with the diameter d, use r = d/2 and get V = π(d/2)^2h = (πd^2h)/4, which matches another common form. The other expressions don’t represent volume: 2πrh is the lateral surface area, and r h misses the necessary factors to cover the circular base.