# Lateral Surface Area

## 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 = 4b^{2}, where b is the base of a cube

Lateral surface area of a sphere is 4πr^{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 = 2πrh, 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 = πrl

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.

### Video Examples: Lateral and Surface Areas of Prisms

### Solved Example on Lateral Surface Area

**Ques: **Find the lateral surface area of a pentagonal prism, if a = 5 cm and b = 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.