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

Find the surface area of the following composite figure. Use pi = 3.14

Right Option : A
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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 ?
Right Option : D
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Explanation
Question : 3

A storage tank consists of circular cylinder with a hemisphere adjoining at either end. If the diameter of the cylinder be 1.4 m and its length be 8 m, the cost of painting it on the outside at the rate of Rs 10 per m2 will be _______________

Right Option : A
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Explanation
 
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