Radii of two circles are in the ratio of 2/3. Find the ratio of their circumferences
since circumference is just a constant multiple of radius, the circumferences are in the same ratio as the radii.
2:3
To find the ratio of the circumferences of two circles, we need to know the ratio of their radii.
Let's assume the radius of the first circle is 'r' units. Since the ratio of their radii is given as 2/3, the radius of the second circle would be (2/3) * r.
The circumference of a circle can be calculated using the formula: C = 2 * π * r, where π (pi) is a mathematical constant approximately equal to 3.14159.
So, the circumference of the first circle would be: C1 = 2 * π * r
And, the circumference of the second circle would be: C2 = 2 * π * (2/3) * r
Now, to find the ratio of their circumferences, we can divide the circumference of the second circle by the circumference of the first circle:
Ratio of circumferences = C2 / C1
Let's substitute the values from above:
Ratio of circumferences = (2 * π * (2/3) * r) / (2 * π * r)
Now, we can cancel out the common terms. The '2' and 'π' would cancel out:
Ratio of circumferences = (2/3) / 1
Therefore, the ratio of the circumferences of the two circles is 2/3.