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Among the following choices, find the difference of the areas of a sector of angle $120 °$ and its corresponding major sector of a circle of radius $21$ cm is

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1386 cm 2

924 cm 2

462 cm 2

231 cm 2

answer is C.

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Detailed Solution

It is given that, the areas of a sector of angle

120 °

.
The major sector of a circle of radius

21

cm.

Area of minor sector

= θ 360 ° × π r 2

Substitute the known values within the formula,

= 120 ° 360 ° × π (21) 2

= 462 c m 2

Area of the circle

= π r 2

= π (21) 2

= 1386 m 2

Area of the major sector

=

Area of circle

−

Area of minor sector

= 1386 − 462

= 924 c m 2

Area of the major sector

−

Area of minor sector

= 924 − 462

= 462 cm 2

Therefore, the area of the major sector is

462 cm^{2}

.
Hence, option 3) is correct.

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Among the following choices, find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm is

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Among the following choices, find the difference of the areas of a sector of angle $120 °$ and its corresponding major sector of a circle of radius $21$ cm is