Question

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

Answer 1

Answer:

$A=15\pi\ units^2$

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

$A=\pi r^{2}$

step 1

Find the Area of the 1st red circle

$r=2/2=1\ unit$ ---> the radius is half the diameter

$A_1=\pi (1)^{2}=\pi\ units^2$

step 2

Find the Area of the 2nd white circle

$r=4/2=2\ units$ ---> the radius is half the diameter

$A_2=\pi (2)^{2}=4\pi\ units^2$

step 3

Find the Area of the 3rd red circle

$r=6/2=3\ units$ ---> the radius is half the diameter

$A_3=\pi (3)^{2}=9\pi\ units^2$

step 4

Find the Area of the 4th white circle

$r=8/2=4\ units$ ---> the radius is half the diameter

$A_4=\pi (4)^{2}=16\pi\ units^2$

step 5

Find the Area of the 5th red circle

$r=10/2=5\ units$ ---> the radius is half the diameter

$A_5=\pi (5)^{2}=25\pi\ units^2$

The total red area is given by

$A=A_5-A_4+A_3-A_2+A_1$

substitute

$A=25\pi-16\pi+9\pi-4\pi+\pi$

$A=15\pi\ units^2$