There are two circular gardens A and B. The circumference of garden A is 1.760 km and the area of garden B is 25 times the area of garden A. Find the circumference of garden B.
If the areas are in the ratio 1:25, the circumferences are in the ratio 1:5
To find the circumference of garden B, we need to first find the radius of both gardens.
The circumference of a circle is given by the formula:
C = 2πr
Given that the circumference of garden A is 1.760 km, we can solve for the radius of garden A:
1.760 = 2πr
Dividing both sides by 2π gives:
r = 1.760 / (2π)
Next, we need to find the radius of garden B. We know that the area of garden B is 25 times the area of garden A.
The area of a circle is given by the formula:
A = πr^2
We know that A(B) = 25 * A(A).
Thus,
πr(B)^2 = 25 * πr(A)^2
Since π is the same in both terms, we can cancel it out. This leads to:
r(B)^2 = 25 * r(A)^2
Taking the square root of both sides, we get:
r(B) = 5 * r(A)
Now that we have the radius of garden B, we can find its circumference using the same formula:
C(B) = 2πr(B)
Substituting the value of r(B), we get:
C(B) = 2π * 5 * r(A)
Finally, substituting the value of r(A), we have:
C(B) = 2π * 5 * (1.760 / (2π))
Simplifying this equation, we find the circumference of garden B:
C(B) = 5 * 1.760
C(B) = 8.800 km
Therefore, the circumference of garden B is 8.800 km.