What is the ratio of the smaller circle's area to the larger circle's area?
Give your answer in fully simplified form. It should look like "x:y", where x and y are replaced by integers.
+655 Assuming that your picture means that the diameter of the smaller square is the radius of the bigger square, here is the solution.
Lets say that the radius of the small circle is x, hence the radius of the larger circle is 2x. Using the area of circles formula: a = πr^2, where r is the radius, the area of the smaller circle is πx^2 and the area of larger circle is 4πx^2
The πx^2 cancels out, leaving us with 1:4.
The simpler solution is that if two shapes are similar, the ratio of their area will be one of the corresponding side's square. In this case, the radius.
+655 Assuming that your picture means that the diameter of the smaller square is the radius of the bigger square, here is the solution.
Lets say that the radius of the small circle is x, hence the radius of the larger circle is 2x. Using the area of circles formula: a = πr^2, where r is the radius, the area of the smaller circle is πx^2 and the area of larger circle is 4πx^2
The πx^2 cancels out, leaving us with 1:4.
The simpler solution is that if two shapes are similar, the ratio of their area will be one of the corresponding side's square. In this case, the radius.
