If a square is inscribed in a circle,the rati | vedclass

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

Question

(B) Let the radius of the circle be $r$.Then,the diameter of the circle $= 2r$.Since the square is inscribed in the circle,the diagonal of the square

Vedclass · Accepted Answer

$\pi: 2$

Vedclass · Answer

(B) Let the radius of the circle be $r$.Then,the diameter of the circle $= 2r$.Since the square is inscribed in the circle,the diagonal of the square is equal to the diameter of the circle.Diagonal of square $= 2r$.Let the side of the square be $a$.Then,$a\sqrt{2} = 2r$,which implies $a = \frac{2r}{\sqrt{2}} = r\sqrt{2}$.Area of the circle $= \pi r^2$.Area of the square $= a^2 = (r\sqrt{2})^2 = 2r^2$.Required ratio $= \frac{	ext{Area of circle}}{	ext{Area of square}} = \frac{\pi r^2}{2r^2} = \frac{\pi}{2}$.Thus,the ratio is $\pi: 2$.

If a square is inscribed in a circle,the ratio of the area of the circle and the square is

Similar Questions

Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the new cuboid to the sum of the surface areas of the three cubes.

$A$ rectangular carpet has an area of $120 \, m^{2}$ and a perimeter of $46 \, m$. The length of its diagonal is ...... $m$.

$A$ steel sphere of radius $4 \, cm$ is drawn into a wire of diameter $4 \, mm$. Find the length of the wire in $mm$.

The ratio of the area of a square to that of the square drawn on its diagonal is

Find the area of the shaded region if the radius of each of the circles is $1\, cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module