Question

The radii of three concentric circles are in the ratio 1:2:3. Find the ratio of the area between the two inner circles to that between the two outer circl

Answer 1

Step-by-step explanation:

I have explained in image

Answer 2

Answer:

Required ratio=1:3:5

Solution:

Given Data:

The radii of three concentric circles in the ratio 1:2:3

According to the question:

To Find:

Find the ratio of the area between the two inner circles to that between the two outer circle.

Step-by-step Explanation:

Step 1:

Let the ratio be n so n, 2n, 3n

$d1 = \frac{r 1}{2}= \frac{r 2}{2}$

$d2 =\frac{r 2}{2}=\frac{2 x}{2}$

$d3 =\frac{r 3}{2}=\frac{3 n}{2}$

Step 2:

Area of first circle$= \pi r^{2} 1=\pi\left(\frac{\mathrm{n}}{2}\right)^{2}=\frac{\pi \mathrm{n} 2}{4} \mathrm{cm}^{2}$

Area of second circle $=\pi r^{2} 2 \quad=\pi\left(\frac{2 \mathrm{n}}{2}\right)^{2}=\pi r^{2} \mathrm{cm}^{2}$

Area of third circle $=\pi r^{2} 3=\pi\left(\frac{3 \mathrm{n}}{2}\right)^{2}=\frac{\pi r^{2}}{2}$

Step 3:

Area of big circle $= \pi r^{2}$

Area of second circle=area of first circle

$=\pi r^{2}-\frac{\pi r^{2}}{4}$=Area of ring

$=4 \pi r^{2}-\pi r^{2}$

$=\frac{4 \pi r^{2}-\pi r^{2}}{4}$ = Area of ring,

$=\frac{4 \pi r^{2}-\pi r^{2}}{4}$

$=\frac{3 \pi r^{2}}{4}=$ Area of ring

Step 4:

Area of second ring = Area of third ring-area of second ring

$=\frac{5 \pi r^{2}}{4} \mathrm{cm}^{2}$

Step 5:

Required Ratio$=\pi r^{2} : \frac{3 \pi r^{2}}{4} : \frac{5 \pi r^{2}}{4} \mathrm{cm}^2$

Required ratio=1:3:5