Let's go step-by-step to detail how we find the length of an arc in a circle.
1. Understand the Problem:
We are given:
- A central angle of 3 radians.
- The radius of the circle is 4 inches.
- We need to find the length of the arc that corresponds to this central angle.
2. Recall the Formula:
The formula to find the length of an arc, [tex]\( s \)[/tex], in a circle when the central angle, [tex]\( \theta \)[/tex], is given in radians is:
[tex]\[
s = r \cdot \theta
\][/tex]
Where:
- [tex]\( r \)[/tex] is the radius of the circle.
- [tex]\( \theta \)[/tex] is the central angle in radians.
3. Substitute the Given Values:
- Here, [tex]\( r = 4 \)[/tex] inches.
- And [tex]\( \theta = 3 \)[/tex] radians.
Plugging in these values into the formula:
[tex]\[
s = 4 \cdot 3
\][/tex]
4. Calculate the Arc Length:
[tex]\[
s = 12
\][/tex]
So, the length of the arc is [tex]\( 12 \)[/tex] inches.
Given the choices:
- [tex]\( s = \frac{3}{4} \)[/tex]
- [tex]\( s = \frac{4}{3} \)[/tex]
- [tex]\( s = 4 + 3 \)[/tex]
- [tex]\( s = 4.3 \)[/tex]
None of these choices directly match our computed value of [tex]\( 12 \)[/tex] inches. However, it's clear that the simplest option corresponding to an arc length derived from given values of radius and angle, which implicitly sums up to an integer (whole number) value, fails a more nuanced choice belonging those decimal/numerical forms supplied. Thus, considering working backwards implicit confirmation utilizing the logical assessment above doesn't straightforward provide cleanly-fitting option other than the corrected confirmed pixelated length [tex]\(12\)[/tex] as just calculated (regardless initial instructional summary extending set bounds numbers as somewhat deviation entity based proving derived 4\*3 sum yielding corrected).
