cone is a solid with a circular base and sides that taper up towards a vertex. A cone is generated from rotating a right triangle, around one leg. A cone has a slant height.


Surface area

Surface area is a two-dimensional measurement that is the total area of all surfaces that bound a solid. The basic unit of area is the square unit. For the surface area of a cone we need the sum of the area of the base and the area of the side.

cone s tot

Surface Area of a Right Cone:


The surface of the base is the surface of a circle and you can use the formula:

cone base

The lateral surface is:

cone s lat

Inversae formulas:

cone inv sl2cone inv sl1

Volume of a cone

Remeber: if you want to find the volume of any solid you must figure out how much space it occupies. The basic unit of volume is the cubic unit.


cone vol

Inversae formula:

cone vol inv


  1. The radius of a cone is 5 inches and the volume is 100π cubic inches. Find the slant height and surface area of this cone. Solution
  2. In a cone, the radius r is given as 2 cm and the slant height s as 6 cm. Find its surface area and volume. Solution
  3. A cone has a slant heightof 8 inches and a surface area of 48π square inches. What are the volume and radius of this cone?
  4. A cone has a height of 6 cm and a volume of  V = 8π cm3. What are the radius and      surface area of this cone?
  5. What is the base area of a cone with radius 9 in. and height 46 in.?
  6. What is the base area of a cone with radius 7 in. and height 52 in.?
  7. Hanna distributed paper hats to children on a Christmas eve. The hats are in the shape of a cone with base radius of 8 cm and a slant height of 18 cm. Find the area of the paper used to make a hat.
  8. A circular cone is 9 in. high. The radius of the base is 12 in. What is the lateral surface area of the cone? Solution
  9. The circumference of the base of a conical tent is 43.96 m and its slant height is11 m. Find the area of the canvas used in making the tent.
  10. A paper cone is 48 cm high and has a radius of 20 cm. Find the area of the paper needed to make the cone.
  11. What is the base area of a cone with radius 6 cm and height 33 cm?
  12. The total surface area of a cone is 240 square cm. If its slant height is four times the radius, then what is the base diameter of the cone?
  13. A circular cone with a base radius of 13 cm has a surface area of 2122.64 cm2.What would be its slant height?

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