An archery target has three regions formed by | vedclass

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

Question

(D) Let the diameters of the concentric circles be $k, 2k$,and $3k$.Therefore,the radii of the concentric circles are $\frac{k}{2}, k$,and $\frac{3k}{

Vedclass · Accepted Answer

$1: 3: 5$

Vedclass · Answer

(D) Let the diameters of the concentric circles be $k, 2k$,and $3k$.Therefore,the radii of the concentric circles are $\frac{k}{2}, k$,and $\frac{3k}{2}$.Area of the inner circle,$A_1 = \pi \left(\frac{k}{2}\right)^2 = \frac{\pi k^2}{4}$.Area of the middle region,$A_2 = \pi(k)^2 - \frac{\pi k^2}{4} = \frac{3\pi k^2}{4}$.Area of the outer region,$A_3 = \pi \left(\frac{3k}{2}\right)^2 - \pi(k)^2 = \frac{9\pi k^2}{4} - \pi k^2 = \frac{5\pi k^2}{4}$.The required ratio of the areas is $A_1 : A_2 : A_3 = \frac{\pi k^2}{4} : \frac{3\pi k^2}{4} : \frac{5\pi k^2}{4} = 1 : 3 : 5$.

An archery target has three regions formed by three concentric circles as shown in the figure. If the diameters of the concentric circles are in the ratio $1: 2: 3$,then find the ratio of the areas of the three regions.

Similar Questions

Find the difference of the areas of two segments of a circle formed by a chord of length $5 \, cm$ subtending an angle of $90^{\circ}$ at the centre.

As shown in the diagram,the side length of square $ABCD$ is $21 \ cm$. $\widehat{APC}$ is an arc of $\odot(B, BA)$ and $\widehat{AQC}$ is an arc of $\odot(D, DA)$. Find the area of the shaded portion. (in $cm^2$)

The ratio of the radii of two circles is $4: 5$. Then,the ratio of their areas is...........

Find the area of the shaded region in the figure,if the radii of the two concentric circles with center $O$ are $7\, cm$ and $14\, cm$ respectively and $\angle AOC = 40^{\circ}$. [Use $\pi = \frac{22}{7}$]

Vedclass Test Series

Exam Paper Generator

Online Exam Module