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The central angles of two sectors of circles of radii $7 cm$ and $21 cm$ are respectively $120 °$ and $40 ° .$ What is the area of the two sectors?

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51.33 c m 2

154 c m 2

50 c m 2

154 c m 2

51 c m 2

150 c m 2

51.33 c m 2

160 c m 2

answer is A.

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Detailed Solution

Given that the central angles of two sectors of circles of radii

7 cm

and

21 cm

are

120 °

and

40 ° .

We have the following formulae,
Area of sector =

π r 2 θ 360 °

Considering the radius 7cm and central angle

120 °

,
Area of the sector will be,

= 227 × 72 × 120 ° 360 ° = 1543 = 51.33 c m 2

Now considering radius 21cm and central angle is

40 °

= 227 × 212 × 40 ° 360 ° = 22 × 21 3 = 22 × 7 = 154 c m 2

Thus, the areas of the two sectors will be

51.33 c m 2

and

154 c m 2

.
Therefore the correct option is 1.

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