You are given two different circles. The diameter of the first circle is the radius of the second circle. What is the ratio of the area of the larger circle to the area of the smaller circle. Your answer should be in the form of a simplified fraction. I have no idea where to start. Please help.
Thank you.
When comparing similar figures (eg. circles with circles, squares with squares, etc.)
Ratio of area
= (ratio of linear dimension)²
In this case,
ratio of diameters=2/1=2
Can you find the ratio of areas?
To find the ratio of the area of the larger circle to the area of the smaller circle, we'll first need to establish the relationship between their radii.
Let's assume the radius of the smaller circle is 'r'. Since the diameter of the first circle is the same as the radius of the second circle, we can say that the diameter of the first circle is '2r'.
The formula for the area of a circle is A = πr^2, where A represents the area and r is the radius. Let's use this formula to find the areas of both circles.
For the smaller circle:
Area of smaller circle = πr^2
For the larger circle:
Area of larger circle = π(2r)^2 = π4r^2
Now, we can calculate the ratio of the area of the larger circle to the area of the smaller circle:
Ratio = Area of larger circle / Area of smaller circle
= π4r^2 / πr^2
= 4
So, the ratio of the area of the larger circle to the area of the smaller circle is 4.
In summary, the area of the larger circle is four times (or 4:1) the area of the smaller circle.