In a circle,the ratio of the areas of two dis | vedclass

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Question

(D) The area of a sector of a circle with radius $r$ and central angle $	heta$ is given by the formula $A = \frac{	heta}{360^\circ} 	imes \pi r^2$.

Vedclass · Accepted Answer

$1:4$

Vedclass · Answer

(D) The area of a sector of a circle with radius $r$ and central angle $	heta$ is given by the formula $A = \frac{	heta}{360^\circ} 	imes \pi r^2$.For two sectors with central angles $	heta_1$ and $	heta_2$ in the same circle,the ratio of their areas is:$\frac{A_1}{A_2} = \frac{(\frac{	heta_1}{360^\circ} 	imes \pi r^2)}{(\frac{	heta_2}{360^\circ} 	imes \pi r^2)} = \frac{	heta_1}{	heta_2}$.Given that the ratio of the areas is $1:4$,we have $\frac{A_1}{A_2} = \frac{1}{4}$.Therefore,$\frac{	heta_1}{	heta_2} = \frac{1}{4}$.Thus,the ratio of the angles at the centre is $1:4$.

In a circle,the ratio of the areas of two distinct minor sectors is $1:4$. Then,the ratio of the angles at the centre for those minor sectors is $\ldots \ldots \ldots \ldots$.

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