The circumferences of two circles are 132 tex | vedclass

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(C) The circumference of a circle is given by $C = 2\pi r$.For the smaller circle,$2 	imes \frac{22}{7} 	imes r_1 = 132 \implies r_1 = \frac{132 	i

Vedclass · Accepted Answer

$1078$

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(C) The circumference of a circle is given by $C = 2\pi r$.For the smaller circle,$2 	imes \frac{22}{7} 	imes r_1 = 132 \implies r_1 = \frac{132 	imes 7}{44} = 21 	ext{ m}$.For the larger circle,$2 	imes \frac{22}{7} 	imes r_2 = 176 \implies r_2 = \frac{176 	imes 7}{44} = 28 	ext{ m}$.The area of a circle is given by $A = \pi r^2$.The difference in areas is $\pi(r_2^2 - r_1^2) = \frac{22}{7} 	imes (28^2 - 21^2)$.Using the identity $a^2 - b^2 = (a - b)(a + b)$,we get $\frac{22}{7} 	imes (28 - 21)(28 + 21) = \frac{22}{7} 	imes 7 	imes 49$.Difference $= 22 	imes 49 = 1078 	ext{ m}^2$.

The circumferences of two circles are $132 \text{ m}$ and $176 \text{ m}$ respectively. What is the difference between the area of the larger circle and that of the smaller circle (in $\text{m}^2$)?

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