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A poor artist on the street makes funny cartoons for children and earns his living. Once he made a comic face by drawing a circle within a circle, the radius of the bigger circle being $30 cm$ and that of smaller being $15 cm$ as shown in the figure. What is the area of the cap given in this figure, the base of the cap being the diameter of the bigger circle?

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900 cm 2

800 cm 2

950 cm 2

700 cm 2

answer is A.

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Detailed Solution

Given that the radius of the bigger circle is

30 cm

and that of smaller is

15 cm

We have the following formulae,
Area of triangle

= 12 b × h

BC = Diameter
BD = 30 cm
AD = 30 cm
BC = Diameter

= 2 B D = 60

Area of the cap will be,

= 12 × base × height = 12 × B C × A D = 12 × 60 × 30

= 900 cm 2

Thus, the area of the cap is

900 cm 2

.
Therefore the correct option is 1.

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