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The two sectors of a circle have the central angles as 120^{0} and 150^{0} respectively. Find the ratio between the areas of the two sectors.

^{2}

= 1/3 x pi xr2

Area of sector with angle 150 = 150/360x pi xr

^{2}

= 5/12x pi xr

^{2}

Ratio of areas of the two sectors=

= (1/3 x pi xr

^{2}) / (5/12x pi xr

^{2})

= (1/3 x pi xr

^{2}) / (5/12x pi xr

^{2})

= (1/3) / (5/12)

= 12/ (5 x 3)

= 4/5 (dividing the numerator and denominator both by 3)

= 4:5

Ans = ratio is 4:5

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