The five circles making up this archery target have diameters of length $2,4,6,8,$ and $10$. What is the total red area?

Simplify your answer as much as you can. You can use pi in your answer if necessary (for example, if the answer were $3\pi$, you could enter "3pi" or "3*pi" or "$3\pi$").

[asy]

size(4cm);

path a=Circle((0,0),5);

path b=Circle((0,0),4);

path c=Circle((0,0),3);

path d=Circle((0,0),2);

path e=Circle((0,0),1);

fill(a, red); fill(b, white); fill(c, red); fill(d, white); fill(e, red);

[/asy]
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Step-by-step explanation:

The picture of the question in the attached figure

we know that

It is given that the diameter of 5 circles making up the archery is 2,4,6,8, and 10.

To determine the total red area, we use the formula for area of the circle

step 1

Find the Area of the 1st red circle

---> the radius is half the diameter

step 2

Find the Area of the 2nd white circle

---> the radius is half the diameter

step 3

Find the Area of the 3rd red circle

---> the radius is half the diameter

step 4

Find the Area of the 4th white circle

---> the radius is half the diameter

step 5

Find the Area of the 5th red circle

---> the radius is half the diameter

The total red area is given by

substitute