IXL Problem Need Help

Question

There is a big circle with the diameter of 8 and a small circle with a diameter of 4

What is the ratio of the area of the smaller circle to the larger circle?

It has to be written as two whole numbers separated by a colon (for example 1:2)

Answer 1

You know the formula for the area of the circle is A_Circle = π*r². We also know that the diameter of a circle is twice its radius. We can write the radius of the big circle as R = D/2 = 8/2 = 4 and the radius of the smaller circle as r = d/2 = 4/2 = 2.

Now we can calculate the areas of the circles.

A_Large = π*R² = π*(4)² = 16π

A_Small = π*r² = π*(2)² = 4π

We can write the ratio as A_Small:A_Large = 4π:16π

This ratio can be simplified by dividing it by a factor of 4π on each side.

Your final answer will be 1:4 or in words, the circle with the larger diameter has an area that is four times larger than the area of the circle with the smaller diameter.

Hope this helps!