The ratio of the area of a sector of a circle | vedclass

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(B) Given,the ratio of the area of the sector to the area of the circle is $1:4$.Area of the circle $= 154 \, cm^2$.Area of the sector $= \frac{1}{4}

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(B) Given,the ratio of the area of the sector to the area of the circle is $1:4$.Area of the circle $= 154 \, cm^2$.Area of the sector $= \frac{1}{4} 	imes 154 = 38.5 \, cm^2$.Since the ratio of the area of the sector to the area of the circle is equal to the ratio of the central angle $	heta$ to $360^{\circ}$,we have $\frac{	heta}{360^{\circ}} = \frac{1}{4}$,which gives $	heta = 90^{\circ}$.Now,find the radius $r$ of the circle: $\pi r^2 = 154 \Rightarrow \frac{22}{7} 	imes r^2 = 154 \Rightarrow r^2 = 49 \Rightarrow r = 7 \, cm$.The perimeter of a sector is given by the formula $P = \frac{	heta}{360^{\circ}} 	imes 2 \pi r + 2r$.Substituting the values: $P = \frac{90^{\circ}}{360^{\circ}} 	imes 2 	imes \frac{22}{7} 	imes 7 + 2 	imes 7$.$P = \frac{1}{4} 	imes 44 + 14 = 11 + 14 = 25 \, cm$.

The ratio of the area of a sector of a circle to the area of the circle is $1:4$. If the area of the circle is $154 \, cm^2$,the perimeter of the sector is ........ $cm$.

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