A **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

- 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
- 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
- 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?
- A cone has a height of 6 cm and a volume of V = 8π cm
^{3}. What are the radius and surface area of this cone? - What is the base area of a cone with radius 9 in. and height 46 in.?
- What is the base area of a cone with radius 7 in. and height 52 in.?
- 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.
- 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
- 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.
- 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.
- What is the base area of a cone with radius 6 cm and height 33 cm?
- 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?
- A circular cone with a base radius of 13 cm has a surface area of 2122.64 cm
^{2}.What would be its slant height?