Which formula gives the surface area of a right circular cone with base radius r and slant height l?

• A. pi r l + pi r^2
• B. 2 pi r l + 2 pi r h
• C. pi r h + pi r^2
• D. 2 pi r l + pi r^2

Answer: (C)

For a right circular cone, the surface area is found by adding the base area and the lateral (side) area. The base area is π r^2, and the lateral area is π r l, where l is the slant height (the length along the side from the tip to the edge of the base). Add them together to get the total surface area: π r l + π r^2.

If you used the vertical height h instead of the slant height, you’d get π r h + π r^2, which isn’t the correct total surface area for a cone. The relation between the three dimensions is l^2 = h^2 + r^2, so l generally differs from h. The other formulas shown either double the lateral term (2π r l) or include a cylinder-like term (2π r h), which aren’t the cone’s surface area.