# how to find the ratio of circumference and the ratio of area of two circles?

question 1: if the lengths of the radii of two circles are 1 and 4 respectively, hat is the ratio of their circumference?of their areas?

question 2: the areas of two circles are 9 cm(squared) and 16 cm, squared .what is the ratio of the radii?

Relevance

RATIO OF THEIR CIRCUMFERENCE :

Circumference of a circle is " 2 pi r "

Substitute thr radius in the formula .

r1 = 1

r2 = 4

2 pi r1

-----------

2 pi r2

= > 1 / 4

RATIO OF THEIR AREAS :

1/ 16

2 ) 9 / 16 IS THE RATIO OF THEIR AREAS

HOPE THIS HELPS................

Circumference of Circle = 2 x radii x pi

Given: 1 and 4

And since the formula for Circumference does not alter for a Circle, your ratio for Circumference is:

1 to 4 or 1/4 or 0.25 depending upon what your teacher wants.

Given: 1 and 4:

It would be 1 x 1 = 1 and 4 x 4 = 16

Your ratio would be: 1 to 16 or 1/16 or 0.0625

As for Given: 9 cm squared and 16 cm squared

You need to square root these which will give you:

3 and 4.

Your ratio is: 3 to 4 or 3/4 or 0.75

• Anonymous
5 years ago

RE:

how to find the ratio of circumference and the ratio of area of two circles?

question 1: if the lengths of the radii of two circles are 1 and 4 respectively, hat is the ratio of their circumference?of their areas?

question 2: the areas of two circles are 9 cm(squared) and 16 cm, squared .what is the ratio of the radii?

Source(s): find ratio circumference ratio area circles: https://tr.im/7BjQF

this gives you ratio of circumference as 1:4.

Area = pi(r^2)

this gives ratio 1:16.

Let the radii of both circles be, r and R. where:

R = 4r (given the 1:4 ratio)

Now find the circumference of each circle:

C = 2πR . . . and . . . c = 2πr

Since R = 4r, substitute it in:

C = 2πR

C = 2π(4r)

C = 8πr

Now since r/R = 1/4, find the ratio of c/C

2πr / 8πr = 1/4

So the circumference is also a 1:4 ratio.

Now do the same with the Area:

A = πR² . . . and a = πr²

A = π(4r)²

A = 16πr²

find the ratio a/A:

πr² / 16πr² = 1/16

So the ratio of areas are 1:16.

#2 works this backwards, you've given the areas and need to find the ratio of radii:

A = πR² . . . and . . .a = πr²

16 = πR² . . . and . . .9 = πr²

16/π = R² . . . and . . . 9/π = r²

4/√π = R . . . and . . . 3/√π = r

calculate r/R

(3/√π) / (4/√π)

(3/√π) * (√π /4)

3/4

The ratio is 3:4.

• Anonymous
5 years ago

A1/A2 = 6(pi)m^2 / 150(pi)m^2 = 1/25 A1/A2 = 1/25 = 1/5^2 since Area is proportional to the radius and likewise, Circumference is proportional to the radius of the circle. If A1?A2 = 1/25 (=1/5^2) then So, c1/c2 = 1/5 <= ANS

• 7 years ago

Find the ratio of the circumferences of two circles, radii 10cm and 15cm.