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

Example of Lateral Surface Area

 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 = prl
Slant height of the cone, l = example of  Lateral Surface Area [l = example of  Lateral Surface Area .]
= 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.

 example of  Lateral Surface Area

Choices:
  • A. 330 cm2
  • B. 95 cm2
  • C. 350 cm2
  • D. 370 cm2

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 cm2.

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