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Circle
O shown below has a radius of 13 inches. To the nearest tenth of an inch, determine the length of the arc,
x, subtended by an angle of
100^(@).
Answer: inches

Circle $O$ shown below has a radius of $13$ inches. To the nearest tenth of an inch, determine the length of the arc, $x$ , subtended by an angle of $100^{\circ}$ . $\newline$ Answer: $\square$ inches

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Circles: word problems

Full solution

Q. Circle

O

shown below has a radius of

13

inches. To the nearest tenth of an inch, determine the length of the arc,

x

, subtended by an angle of

100^{\circ}

.

\newline

Answer:

\square

inches

Identify formula: Identify the formula to calculate the length of an arc. $\newline$ The length of an arc $L$ in a circle is given by the formula $L = (\theta/360) \times 2\pi r$ , where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.
Plug values: Plug in the given values into the formula. $\newline$ Here, $\theta = 100$ degrees and $r = 13$ inches. We will use $\pi \approx 3.14$ for our calculations. $\newline$ $L = \left(\frac{100}{360}\right) \times 2 \times 3.14 \times 13$
Calculate fraction: Calculate the fraction of the circle that the arc length represents. $\newline$ $100$ degrees is $\frac{100}{360}$ of the full circle. $\newline$ $\frac{100}{360} = \frac{5}{18}$
Calculate length: Calculate the arc length. $\newline$ $L = \frac{5}{18} \times 2 \times 3.14 \times 13$ $\newline$ $L = \frac{5}{18} \times 2 \times 3.14 \times 13$ $\newline$ $L = \frac{5}{9} \times 3.14 \times 13$ $\newline$ $L = 5 \times 3.14 \times 13 / 9$ $\newline$ $L = 15.7 \times 13 / 9$ $\newline$ $L = 204.1 / 9$ $\newline$ $L \approx 22.677777...$
Round result: Round the result to the nearest tenth of an inch. $\newline$ $L \approx 22.7$ inches

More problems from Circles: word problems

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\newline

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1

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and the other leg measures

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Find the volume of a right circular cone that has a height of

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\newline

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Question

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and a base with a diameter of

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\newline

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