In the cone volume formula V = (1/3) π r^2 h, which variable is squared?

In the cone volume formula V = (1/3) π r^2 h, which variable is squared?

• A. r
• B. h
• C. π
• D. none of the above

Answer: (A)

The squared quantity comes from the base area. The cone’s volume is one-third of the base area times the height, and the base is a circle with area πr^2. Since the area of a circle depends on the square of the radius, the r is the part that’s squared. The height appears only once as h, not squared, and π is just a constant. So the radius is the variable that is squared.

The squared quantity comes from the base area. The cone’s volume is one-third of the base area times the height, and the base is a circle with area πr^2. Since the area of a circle depends on the square of the radius, the r is the part that’s squared. The height appears only once as h, not squared, and π is just a constant. So the radius is the variable that is squared.