If the ratio between the two circles is 9:16,find
i)the ratio between the radii
ii)the ratio between their circumference
Thank you
i) √(9/16) = 3/4
ii) since C∝r, the same ratio.
To find the ratio between the radii of the two circles, we can use the fact that the ratio of the areas of two circles is equal to the square of the ratio of their radii.
Since the ratio of the two circles is given as 9:16, we can say that the ratio of their areas is also 9:16. This means that if we let the radius of the first circle be r, the area of the first circle will be πr^2, and the area of the second circle will be π(R^2), where R is the radius of the second circle.
Therefore, we have:
(πr^2) / (πR^2) = 9/16
Now, we can cancel out the π and solve for the ratio of the radii:
r^2 / R^2 = 9/16
Taking the square root of both sides to isolate the ratio of the radii, we get:
(r/R) = √(9/16)
Simplifying the square root, we have:
(r/R) = 3/4
So, the ratio between the radii of the two circles is 3:4.
To find the ratio between their circumferences, we can use the fact that the circumference of a circle is directly proportional to its radius.
Therefore, if the ratio between the radii is 3:4, the ratio between their circumferences will also be 3:4.
Hence, the ratio between the circumferences of the two circles is 3:4.