the area of circle B is 36 times greater than the area of circle A. The radius of circle B is 30. what is the radius of circle A
Ab = pi*r^2 = 3.14 * 30^2 = 2837.4 = Area of B.
Ab = Aa + 30Aa = 2827.4
31Aa = 2827.4
Aa = 91.2.
Aa = pi*r^2 = 91.2
r^2 = 91.2 / pi = 29.03
r = 5.4 = Radius of circle A.
Correction: Ab = 2827.4.
To find the radius of circle A, we need to first compare the areas of circle A and B. The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
Let's denote the radius of circle A as r_A and the radius of circle B as r_B. Given that the area of circle B is 36 times greater than the area of circle A, we can express this mathematically as:
A_B = 36 * A_A
Replacing the area formula, we have:
πr_B^2 = 36 * πr_A^2
Canceling out π on both sides gives us:
r_B^2 = 36r_A^2
Taking the square root of both sides gives:
r_B = 6r_A
We are also given that the radius of circle B is 30 (r_B = 30). We can substitute this into our equation to find the radius of circle A:
30 = 6r_A
Divide both sides by 6:
r_A = 5
Therefore, the radius of circle A is 5.