THE area of circle B is 25 times greater than the area of circle A. The radius of circle A is 3. What is the radius of circle B?
the area grows as the square of the radius.
So, the radius grows as the square root of the area.
Since areaB/areaA = 25,
radiusB/radiusA = √25 = 5
To find the radius of circle B, we first need to calculate the area of circle A and then use that information to determine the radius of circle B.
The formula to calculate the area of a circle is: A = π * r^2, where A is the area and r is the radius.
Given that the radius of circle A is 3, we can calculate its area using the formula:
A = π * (3^2) = π * 9 = 9π
Since the area of circle B is 25 times greater than the area of circle A, we can express it as:
Area of B = 25 * Area of A
Substituting the value of the area of A into the equation, we get:
Area of B = 25 * (9π) = 225π
To find the radius of circle B, we need to reverse the formula for calculating the area:
Area of B = π * (r^2)
Now we can solve for the radius of circle B:
225π = π * (r^2)
Divide both sides of the equation by π to isolate the radius:
225 = r^2
Take the square root of both sides to find the radius:
r = √225 = 15
Therefore, the radius of circle B is 15.