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 radius $42 \ cm$,a minor arc subtends an angle of $60^{\circ}$ at the centre. Find the area of the minor sector and the minor segment corresponding to this arc. (Use $\sqrt{3} = 1.73$)

Find the circumference and the area of a circular ground with radius $77\, m$.

Area of the largest triangle that can be inscribed in a semi-circle of radius $r$ units is

The length of the minute hand of a clock is $10.5 \, cm$. Find the area of the region swept by it between $2.25 \, PM$ and $2.40 \, PM$. (in $cm^2$)

The area of a minor sector of $\odot(P, 30)$ is $300 \, cm^2$. The length of the arc corresponding to it is .......... $cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module