Surface areas and Volumes – Examples on Frustum of a cone

Table of Contents

Table of Contents

In the previous segment, we learnt about the frustum of a cone formula in detail. In this segment, we will solve an example based on it.

Example

Q. The radii of the circular ends of a frustum of a cone of height 3cm are 8cm and 4cm respectively. Find the total surface area of the frustum.

Figure 1

Solution:

Height of the frustum (h) = 3 cm

Radius of the larger base of the frustum

Radius of the smaller base of the frustum

By considering the upper part of the cone from which the frustum is derived as shown below, we get,

Figure 2

are the parameters as shown in the figure.

… (i)

and … (ii)

For a frustum,

… (iii)

From (ii) and (iii),

In the above figure, △AOB is a right-angled triangle.

∴ By Pythagoras theorem,

Surface area of frustum =

∴ Surface area of frustum =

Thus, the total surface area of the given frustum is 440 sq. cm.

In the next segment of Class 10 Maths, we will learn about Statistics.