Find the radius of a circle that has an arclength of 17π/12 inches when a central angle measures 7π/9. Round to the nearest hundredth.
s = rθ
so, plug in your numbers
7/9 π r = 17/12 π
r = 17/12 * 9/7 = ____
[central angle (in radians)] * radius = arc length
r = (17 π / 12) / (7 π / 9) ... inches
@oobleck so would it be s=1.82?
I guess.
I assumed you could use your calculator.
lemme see.... yep 1.82
To find the radius of a circle, we can use the formula:
Arc Length = r * θ
Where:
- Arc Length is the length of the arc in inches,
- r is the radius of the circle in inches, and
- θ is the central angle in radians.
In this case, the Arc Length is given as 17π/12 inches and the central angle is 7π/9. We can substitute these values into the formula and solve for r.
17π/12 = r * 7π/9
To solve for r, we can start by canceling out the π (pi) terms:
17/12 = r * 7/9
Next, we can rearrange the equation to isolate r:
r = (17/12) / (7/9)
To divide fractions, we multiply by the reciprocal of the divisor:
r = (17/12) * (9/7)
Multiply the numerators and denominators:
r = (17 * 9) / (12 * 7)
r = 153 / 84
Divide both numerator and denominator by their greatest common divisor, which is 3:
r = 51 / 28
To round to the nearest hundredth, we divide the numerator by the denominator:
r ≈ 1.821
Therefore, the radius of the circle is approximately 1.82 inches.