What is the volume formula for a right circular cylinder with radius r and height h?

What is the volume formula for a right circular cylinder with radius r and height h?

• A. V=πr²h
• B. V=2πrh
• C. V=πr²
• D. V=4/3πr^3

Answer: (A)

Volume is found by multiplying the area of the base by the height. For a right circular cylinder, the base is a circle with area πr^2, and the height is h, so the volume is V = πr^2h. You can picture filling the cylinder with many thin discs; each disc has area πr^2 and thickness dh, and summing them up gives πr^2h. The other expressions correspond to different quantities: 2πrh is the side surface area, πr^2 is just the base area, and 4/3πr^3 is the volume of a sphere.

Volume is found by multiplying the area of the base by the height. For a right circular cylinder, the base is a circle with area πr^2, and the height is h, so the volume is V = πr^2h. You can picture filling the cylinder with many thin discs; each disc has area πr^2 and thickness dh, and summing them up gives πr^2h. The other expressions correspond to different quantities: 2πrh is the side surface area, πr^2 is just the base area, and 4/3πr^3 is the volume of a sphere.