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 = 4b2, where b is the base of a cube
- Lateral surface area of a sphere is 4pr2, where r is the radius of the sphere.
- Lateral surface area of a cone = p ◊ r ◊ l, where r and l are the radius and slant height of the cone
- Lateral surface area of a cylinder = 2prh, 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
Video Examples: Lateral and Surface Areas of Prisms
Example of Lateral Surface Area
Letís 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 = prl
Slant height of the cone, l = [l =.]
= 10 yd
Lateral surface area = 3.14 ◊ 6 ◊ 10 [As r = 6 and h = 10]
So, the lateral surface area of the cone = 188.4 sq yd.
Solved Example on Lateral Surface Area
Ques: Find the lateral surface area of a pentagonal prism, if a = 5 cm and b = 14 cm.
A. 330 cm2
B. 95 cm2
C. 350 cm2
D. 370 cm2
Correct Answer: C
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 cm2.