Answer:
The center is
of the whole target.
Step-by-step explanation:
Given:
Diameter of the center = 5 inches
Diameter of the whole target = 25 inches
We need to find the part of the center to the whole target.
Solution,
Firstly we will find out the areas of center and whole target.
For center;
Diameter = 5 in
Radius of circle is equal to half of the diameter.
radius = ![\frac{diameter}{2}=\frac{5}{2}=2.5\ in](https://tex.z-dn.net/?f=%5Cfrac%7Bdiameter%7D%7B2%7D%3D%5Cfrac%7B5%7D%7B2%7D%3D2.5%5C%20in)
Now we know that the area of circle is equal to π times square of the radius.
framing in equation form, we get;
Area =
For whole target;
Diameter = 25 in
Radius of circle is equal to half of the diameter.
radius = ![\frac{diameter}{2}=\frac{25}{2}=12.5\ in](https://tex.z-dn.net/?f=%5Cfrac%7Bdiameter%7D%7B2%7D%3D%5Cfrac%7B25%7D%7B2%7D%3D12.5%5C%20in)
Now we know that the area of circle is equal to π times square of the radius.
framing in equation form, we get;
Area = ![\pi \times12.5^2](https://tex.z-dn.net/?f=%5Cpi%20%5Ctimes12.5%5E2)
Now to find the part of the center to the whole target we will divide Area of center with Area of the target.
framing in equation form we get;
the part of the center to the whole target = ![\frac{\pi \times2.5^2}{\pi \times12.5^2}= \frac{6.25}{156.25} = \frac{1}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20%5Ctimes2.5%5E2%7D%7B%5Cpi%20%5Ctimes12.5%5E2%7D%3D%20%5Cfrac%7B6.25%7D%7B156.25%7D%20%3D%20%5Cfrac%7B1%7D%7B25%7D)
Hence the center is
of the whole target.