Which expression is the correct volume formula for a cone?

Which expression is the correct volume formula for a cone?

• A. V=1/3πr²h
• B. V=4/3πr³
• C. A=πr²
• D. V=1/3Bh

Answer: (A)

The volume of a cone comes from comparing it to a cylinder that has the same base and height. Since the cone occupies about one third of that cylinder’s volume, its volume is one third of the base area times the height. For a circular base, the base area is π r^2, so V = (1/3) π r^2 h. This is the standard form used for cones. Another general way to express the same idea is V = (1/3) B h, where B is the base area; with a circular base, B = π r^2, giving the same result. The other expressions correspond to different shapes or different quantities (such as the sphere’s volume or a circle’s area).

The volume of a cone comes from comparing it to a cylinder that has the same base and height. Since the cone occupies about one third of that cylinder’s volume, its volume is one third of the base area times the height. For a circular base, the base area is π r^2, so V = (1/3) π r^2 h. This is the standard form used for cones. Another general way to express the same idea is V = (1/3) B h, where B is the base area; with a circular base, B = π r^2, giving the same result. The other expressions correspond to different shapes or different quantities (such as the sphere’s volume or a circle’s area).