# Cone

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. Surface Area of a Right Cone: The surface of the base is the surface of a circle and you can use the formula: The lateral surface is: Inversae formulas:  ### 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.  Inversae formula: #### Exercises

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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