Surface Area of Composite Figures

Concept Explanation

Surface Area of Composite Figures

Surface area of Composite Figures:

Example: A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.

Solution: Let r be the radius of the hemisphere and h be the height of the conical part of the toy. Then, r = 4.2 cm, height of cone = (10.2 - 4.2) cm = 6 cm. Also, radius of the base of the cone = 4.2 cm

$large therefore$ Surface Area of Composite Figure = CSA of cone + CSA of hemisphere = = $large frac{pi r^{2}}{3}(h + 2r)cm^{3}$

= $large frac{1}{3}times frac{22}{7}times 4.2times 4.2 times (6+2times 4.2)cm^{3}$

= $large frac{1}{3}times frac{22}{7}times 4.2times 4.2 times 14.4 cm^{2} =266.11 cm^{3}$

Composite Figures

A figure (or shape) that can be divided into more than one of the basic figures is said to be a composite figure (or shape).

For example, figure ABCD is a composite figure as it consists of two basic figures. That is, a figure is formed by a rectangle and triangle as shown below.

The area of a composite figure is calculated by dividing the composite figure into basic figures and then using the relevant area formula for each basic figure.

Example:- Find the area of the following composite figure:

Solution:

The figure can be divided into a rectangle and triangle as shown below.

So, the area of the composite figure is 216 cm2.

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Three cubes each of side 5 cm are joined end to end. Find the surface area of the resulting cuboid.
A. 350	B. 250	C. 345	D. 355
Right Option : A
View Explanation

Question : 2

A cylindrical solid with height 'h' and radius 'r' is surmounted by the conial solids from both the sides. If the volime of the conial slids is the same with slant height 'l', which of the following is the surface area of the whole structure ?

$large 2pi: (h+l +2r): cm^2$

$large 2pi r: (h+l +r): cm^2$

$large 2pi: (h+l ): cm^2$

$large 2pi r (h+l ): cm^2$

Right Option : D

View Explanation

Question : 3

Find the surface area of the following composite figure. Use $pi = 3.14$
A. 637.42 sq units	B. 367.42 sq units	C. 363.42 sq units	D. 673.42 sq units
Right Option : A
View Explanation

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Real Numbers I

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Pair of Linear Equations I

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Introduction to Trigonometry

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Surface Area and Volume I

Surface Area and Volume II

Areas Related to Circles

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