Two minor sectors of two distinct circles hav | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The area of a sector of a circle is given by the formula $A = \frac{	heta}{360^\circ} 	imes \pi r^2$.Let the radii of the two circles be $r_1$ a

Vedclass · Accepted Answer

$2:3$

Vedclass · Answer

(C) The area of a sector of a circle is given by the formula $A = \frac{	heta}{360^\circ} 	imes \pi r^2$.Let the radii of the two circles be $r_1$ and $r_2$ and the central angles be $	heta_1$ and $	heta_2$.Given that $	heta_1 = 	heta_2 = 	heta$.The ratio of the areas of the two sectors is given as $\frac{A_1}{A_2} = \frac{4}{9}$.Substituting the formula,we get $\frac{\frac{	heta}{360^\circ} 	imes \pi r_1^2}{\frac{	heta}{360^\circ} 	imes \pi r_2^2} = \frac{4}{9}$.Simplifying the expression,we have $\frac{r_1^2}{r_2^2} = \frac{4}{9}$.Taking the square root on both sides,we get $\frac{r_1}{r_2} = \sqrt{\frac{4}{9}} = \frac{2}{3}$.Therefore,the ratio of the radii is $2:3$.

Two minor sectors of two distinct circles have the measure of the angle at the centre equal. If the ratio of their areas is $4:9,$ then the ratio of the radii of the circles is ........

Similar Questions

In a circle with radius $7 \, cm$,the perimeter of a minor sector is $\frac{86}{3} \, cm$. Then,the area of that minor sector is $\ldots \ldots \ldots \ldots cm^2$.

In $\odot(O, 12)$, minor $\widehat{ACB}$ subtends an angle of measure $30^{\circ}$ at the centre. Then, the length of major $\widehat{ADB}$ is $\ldots \ldots \ldots \text{ cm}$. (in $\pi$)

The diameter of a circular garden is $210 \,m$. Inside it,all along the boundary,there is a path of uniform width $7 \,m$. Then,the area of the path is $\ldots \ldots \ldots \ldots \,m^2$.

If the radius of a circle is increased by $10 \%,$ its area will increase by $\ldots \ldots \ldots . \%$

Find the area of the sector of a circle of radius $5\, cm$,if the corresponding arc length is $3.5\, cm$. (in $cm^2$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module