## Cone -Geometry Formulas

### Cone

A cone is a three-dimensional figure with one circular base. A curved surface connects the base and the vertex.

### Slant Height

The distance from the top of a cone, down the side to a point on the edge of the base.

Slant Height, l = √(r2+h2)

### Volume of the Cone

Volume(V) = ⅓ πr2h cubic units

### Example:

Find the volume of the cone whose base radius is 6 cm and height is 12 cm.

### Solution:

volume of the cone= (1/3) x (22/7) x 62 x 12

= 9504/21

= 452.57 cubic cm.

### Surface Area of the Cone:

The total surface area of the cone = πrl + πr2

Or

Area = πr(l + r)

### Example:

Find the total surface area of a right cone if the radius is 6 inches and the slant height is 10 inches.

### Solution:

T.S.A = π(6)(10)+π(6)2

=60π+36π

=96π inches2

≈301.59 inches2

### Curved Surface Area of Cone

Curved Surface Area of Cone = πrl

### Example:

Find the lateral surface area of a right cone if the radius is 44 cm and the slant height is 55 cm.

L.S.A=π(4)(5)

= 20π

≈ 62.82 cm2