To determine the area of the target, we need to find the total area that the bull's-eye covers and then use the given information to find the total area of the target.
1. Find the Area of the Bull's-eye:
- The diameter of the bull's-eye is 4 inches.
- Therefore, the radius [tex]\( r \)[/tex] of the bull's-eye is [tex]\( \frac{4}{2} = 2 \)[/tex] inches.
- The area [tex]\( A \)[/tex] of a circle is given by the formula [tex]\( A = \pi r^2 \)[/tex].
- Substituting the radius:
[tex]\[
A_{\text{bullseye}} = \pi \times 2^2 = \pi \times 4 = 4\pi
\][/tex]
2. Determine the Total Area of the Target:
- It is given that the bull's-eye covers 20% of the target.
- This means the area of the bull's-eye is 20% of the total area of the target.
- Let [tex]\( A_{\text{target}} \)[/tex] be the area of the target. According to the problem, [tex]\( 4\pi \)[/tex] is 20% of [tex]\( A_{\text{target}} \)[/tex].
- Therefore:
[tex]\[
4\pi = 0.2 \times A_{\text{target}}
\][/tex]
- To find [tex]\( A_{\text{target}} \)[/tex], solve for [tex]\( A_{\text{target}} \)[/tex] by dividing both sides of the equation by 0.2:
[tex]\[
A_{\text{target}} = \frac{4\pi}{0.2} = 4\pi \times \frac{1}{0.2} = 4\pi \times 5 = 20\pi
\][/tex]
Given the calculations above, the area of the target is [tex]\( 20\pi \)[/tex] square inches.
Thus, the correct answer is:
B. 32π
