Certainly! Let's solve the problem step-by-step.
1. Identify the diameter of the bull's-eye:
- The diameter of the bull's-eye is given as 4 inches.
2. Calculate the radius of the bull's-eye:
- The radius [tex]\( r \)[/tex] is half of the diameter.
[tex]\[
r = \frac{d}{2} = \frac{4}{2} = 2 \text{ inches}
\][/tex]
3. Calculate the area of the bull's-eye:
- The area [tex]\( A \)[/tex] of a circle is given by the formula:
[tex]\[
A = \pi r^2
\][/tex]
Using the radius 2 inches:
[tex]\[
A = \pi \times (2^2) = \pi \times 4 = 4\pi \text{ square inches}
\][/tex]
4. Determine the percentage of the bull's-eye:
- The bull's-eye covers 20% (or 0.20) of the total area of the target.
5. Calculate the total area of the target:
- Let's denote the total area of the target by [tex]\( T \)[/tex].
- Since the bull's-eye area is 20% of the total target area:
[tex]\[
0.20T = 4\pi
\][/tex]
- To solve for [tex]\( T \)[/tex], divide both sides by 0.20:
[tex]\[
T = \frac{4\pi}{0.20} = 4\pi \div 0.20 = 4\pi \times \frac{1}{0.20} = 4\pi \times 5 = 20\pi \text{ square inches}
\][/tex]
6. Identify the correct answer:
- The area of the target is [tex]\( 20\pi \text{ square inches} \)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{20\pi}
\][/tex]
So, option D. 20π is the right answer.
