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Circle O shown below has an arc of length 3 inches subtended by an angle of 1.5 radians. Find the length of the radius, x, to the nearest tenth of an inch. Answer: inches

Circle O O shown below has an arc of length 33 inches subtended by an angle of 11.55 radians. Find the length of the radius, x x , to the nearest tenth of an inch.\newlineAnswer: □\square inches

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Full solution

Q. Circle O O shown below has an arc of length 33 inches subtended by an angle of 11.55 radians. Find the length of the radius, x x , to the nearest tenth of an inch.\newlineAnswer: □\square inches
  1. Understand Relationship: Understand the relationship between arc length, radius, and central angle in radians.\newlineThe formula to find the arc length ss of a circle given the radius rr and the central angle in radians θ\theta is s=rθs = r\theta.\newlineHere, we are given the arc length s=3s = 3 inches) and the central angle θ=1.5\theta = 1.5 radians), and we need to find the radius rr.
  2. Rearrange Formula: Rearrange the formula to solve for the radius.\newlineTo find the radius, we rearrange the formula to r=sθ.r = \frac{s}{\theta}.
  3. Substitute Values: Substitute the given values into the rearranged formula. r=3 inches1.5 radiansr = \frac{3 \, \text{inches}}{1.5 \, \text{radians}}
  4. Calculate Radius: Calculate the radius. r=3 inches1.5 radians=2 inchesr = \frac{3 \text{ inches}}{1.5 \text{ radians}} = 2 \text{ inches}
  5. Round to Nearest Tenth: Round the radius to the nearest tenth of an inch.\newlineSince the radius is already a whole number, rounding to the nearest tenth gives us the same value, 2.02.0 inches.

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