Question

The diameters of two circles are in the ratio 1:3. Find the ratio of their CIrcumference and areas.​

Answer 1

Step-by-step explanation:

circumference = 3 x diameter

ratio of circumference= 3x1 : 3x3 = 3 : 9

areas = π x d

ratio of areas = π x 1 : π x 3

Answer 2

Given, ratio of the diameters of two circles = 1:3

Let the diameter of one of the circles be 1×d = d

and let the diameter of the other circle be 3×d = 3d

Now,

Radius (r) of the circle with diameter d = d/2

Radius (r1) of the circle with diameter 3d = 3d/2

Now,

Circumference of the circle with diameter d =

$2 \: \pi \: r$

$= 2 \: \pi \: \frac{d}{2}$

$= \pi \: d$

Circumference of the circle with diameter 3d =

$2 \: \pi \: r1$

$= 2 \: \pi \: \frac{3d}{2}$

$= 3 \: \pi \: d$

Therefore, ratio of their circumference=

$= \frac{\pi \: d}{3 \: \pi \: d}$

$= \frac{1}{3}$

= 1 : 3 (Answer)

Now,

Area of the circle with diameter d =

$\pi \: {r}^{2}$

$= \pi \: { (\frac{d}{2}) }^{2}$

$= \frac{\pi \: {d}^{2} }{4}$

Area of the circle with diameter 3d =

$\pi \: {(r1)}^{2}$

$= \pi \: {( \frac{3d}{2}) }^{2}$

$= \frac{9 \: \pi \: {d}^{2} }{4}$

Now, ratio of ther areas =

$\frac{\pi \: {d}^{2} }{4} \times \frac{4}{9 \: \pi \: {d}^{2} }$

= 1/9

= 1 : 9 (Answer)