**Definition of Lateral Surface Area**

- Lateral surface area in a solid is the sum of the surface areas of all its faces excluding the base of the solid.

**More about Lateral Surface Area**

- Lateral surface area of a cube = 4
*b*2, where*b*is the base of a cube - Lateral surface area of a sphere is 4
*πr*^{2}, where*r*is the radius of the sphere. - Lateral surface area of a cone =
*π*×*r*×*l*, where*r*and*l*are the radius and slant height of the cone - Lateral surface area of a cylinder = 2
*π**rh*, where*r*is the radius and*h*is the height of the cylinder - Lateral surface area of the right triangular pyramid = 3 × area of lateral faces
- Lateral surface area of a pentagonal prism = 5 × area of each rectangle

**Example of Lateral Surface Area**

- Let’s find out the lateral surface of a cone that has a base radius (
*r*) of length 6 yd and a height (*h*) of 8 yd.

Lateral surface area of the cone =*π**rl*

Slant height of the cone,*l*= [*l*=.]

= 10 yd

Lateral surface area = 3.14 × 6 × 10 [As*r*= 6 and*h*= 10]

= 188.4

So, the lateral surface area of the cone = 188.4 sq yd.

**Solved Example on Lateral Surface Area**

Find the lateral surface area of a pentagonal prism, if

a= 5 cm andb= 14 cm.

Choices:

A. 330 cm^{2}

B. 95 cm^{2}

C. 350 cm^{2}

D. 370 cm^{2}

Correct Answer: C

Solution:

Step 1:In the given figure, the base of the prism is a regular pentagon.

Step 2:All five rectangles are congruent.

Step 3:Lateral surface area of the prism = 5 × area of each rectangle

Step 4:= 5 × 5 × 14 [Substitute the values.]

Step 5:= 350 [Simplify.]

Step 6:Lateral surface area of the pentagonal prism = 350 cm^{2}.

**Related Terms for Lateral Surface Area**

- Area
- Base
- Breadth
- Cone
- Cube
- Cylinder
- Face
- Height
- Prism
- Pyramid
- Radius
- Solid
- Sphere
- Surface Area