Which expression gives the volume of a cone?

Which expression gives the volume of a cone?

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

Answer: (D)

Volume of a cone comes from taking one-third of the product of its base area and its height. For a cone with a circular base, the base area is πr^2, so the volume is V = (1/3) π r^2 h. This shows how the size of the base and the height determine how much space the cone occupies. The other forms don’t express the cone’s volume in terms of its radius and height: one is the volume formula for a sphere, another is just the base area, and a general form V = (1/3) B h uses the base area symbol without substituting πr^2. The explicit expression in terms of r and h is the one that matches the cone’s geometry, V = (1/3) π r^2 h.

Volume of a cone comes from taking one-third of the product of its base area and its height. For a cone with a circular base, the base area is πr^2, so the volume is V = (1/3) π r^2 h. This shows how the size of the base and the height determine how much space the cone occupies. The other forms don’t express the cone’s volume in terms of its radius and height: one is the volume formula for a sphere, another is just the base area, and a general form V = (1/3) B h uses the base area symbol without substituting πr^2. The explicit expression in terms of r and h is the one that matches the cone’s geometry, V = (1/3) π r^2 h.