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

       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 = 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.

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.