Which expression gives the surface area of a cone in terms of radius r and slant height s?

Which expression gives the surface area of a cone in terms of radius r and slant height s?

• A. π r s + π r^2
• B. π r s
• C. 2π r s + π r^2
• D. π r (s + r)

Answer: (A)

The surface area of a cone includes the base and the curved surface. The base is a circle with area πr^2, and the curved (lateral) surface area is πrs. Adding them gives the total surface area: πrs + πr^2. That matches the given expression. You can also see it by factoring: πr(s + r), which is the same value. The other options don’t add the base area or double the lateral area, so they don’t represent the cone’s total surface area.

The surface area of a cone includes the base and the curved surface. The base is a circle with area πr^2, and the curved (lateral) surface area is πrs. Adding them gives the total surface area: πrs + πr^2. That matches the given expression. You can also see it by factoring: πr(s + r), which is the same value. The other options don’t add the base area or double the lateral area, so they don’t represent the cone’s total surface area.