The ratio of the areas of two circles is 25: | vedclass

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

Question

(A) Let the radii of the two circles be $r_1$ and $r_2$ respectively.The area of a circle is given by the formula $A = \pi r^2$.The ratio of the areas

Vedclass · Accepted Answer

$5: 6$

Vedclass · Answer

(A) Let the radii of the two circles be $r_1$ and $r_2$ respectively.The area of a circle is given by the formula $A = \pi r^2$.The ratio of the areas is given as $\frac{A_1}{A_2} = \frac{\pi r_1^2}{\pi r_2^2} = \frac{r_1^2}{r_2^2} = \frac{25}{36}$.Taking the square root of both sides,we get $\frac{r_1}{r_2} = \sqrt{\frac{25}{36}} = \frac{5}{6}$.The circumference of a circle is given by $C = 2\pi r$.The ratio of their circumferences is $\frac{C_1}{C_2} = \frac{2\pi r_1}{2\pi r_2} = \frac{r_1}{r_2}$.Therefore,the ratio of their circumferences is $5: 6$.

The ratio of the areas of two circles is $25: 36$. Then,the ratio of their circumferences is:

Similar Questions

In a circle with centre $O$,$\overline{OA}$ and $\overline{OB}$ are radii perpendicular to each other. The perimeter of the sector formed by these radii is $75 \, cm$. Find the area of the corresponding minor segment. (in $cm^2$)

The side length of square $ABCD$ shown in the diagram is $42 \ cm$. The shaded design is formed by drawing semicircles on all the sides of the square. Find the area of the shaded design in $cm^2$.

If the circumference of a circle and the perimeter of a square are equal,then

The ratio of the areas of the circles with radii $8 \, cm$ and $12 \, cm$ is $\ldots \ldots \ldots \ldots .$

In a circle with radius $21 \ cm$,the perimeter of a minor sector is $64 \ cm$. Then,the length of the arc of that sector is $\ldots \ cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module