Question

The center on a target has a diameter of 5 inches. The whole target has a diameter of 25 inches. Complete the explanation for what part of the whole target is the center.

Answer 1

Answer:

The center is $\frac{1}{25}$ 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 = $\frac{diameter}{2}=\frac{5}{2}=2.5\ in$

Now we know that the area of circle is equal to π times square of the radius.

framing in equation form, we get;

Area = $\pi \times{2.5}^2$

For whole target;

Diameter = 25 in

Radius of circle is equal to half of the diameter.

radius = $\frac{diameter}{2}=\frac{25}{2}=12.5\ in$

Now we know that the area of circle is equal to π times square of the radius.

framing in equation form, we get;

Area = $\pi \times12.5^2$

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 = $\frac{\pi \times2.5^2}{\pi \times12.5^2}= \frac{6.25}{156.25} = \frac{1}{25}$

Hence the center is $\frac{1}{25}$ of the whole target.