let the radius of each of the smaller circles be r
so the radius of the larger circle is 3r
Ï€(3r)^2 = 81Ï€
9Ï€r^2 = 81Ï€
r^2 = 9
r=3
Circumf of smaller circle = 2Ï€r = 6Ï€
so the radius of the larger circle is 3r
Ï€(3r)^2 = 81Ï€
9Ï€r^2 = 81Ï€
r^2 = 9
r=3
Circumf of smaller circle = 2Ï€r = 6Ï€
1. We know that the area of the large circle is 81π square units. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Therefore, we can set up the equation 81π = π(R/2)^2, where R is the radius of the large circle.
2. Simplifying the equation, we have 81 = (R/2)^2.
Taking the square root of both sides gives us √81 = √(R/2)^2.
Simplifying further, we get 9 = R/2.
3. Now that we know the radius of the large circle (R), we need to find the radius of one of the smaller circles. Since the centers of the smaller circles are collinear, we can determine that the diameter of the large circle is equal to the sum of the diameters of the three smaller circles.
The diameter of the large circle is equal to 2R, and the diameter of one of the smaller circles is equal to 2r, where r is the radius of the small circle.
4. From step 3, we have the equation 2R = 2r + 2r + 2r, since there are three smaller circles.
Simplifying, we get 2R = 6r.
5. Substituting the value of R we found in step 2 (R = 18), we have 2(18) = 6r.
Simplifying further, we get 36 = 6r.
6. Dividing both sides of the equation by 6 gives us r = 6.
7. Now that we know the radius of one of the smaller circles (r = 6), we can find the circumference of the circle using the formula C = 2Ï€r.
Substituting the value of r, we get C = 2Ï€(6) = 12Ï€ units.
Therefore, the circumference of one of the smaller circles is 12Ï€ units.