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Circle
O shown below has a radius of 27 inches. To the nearest tenth of an inch, determine the length of the arc,
x, subtended by an angle of 1.2 radians.
Answer:
inches

Circle $O$ shown below has a radius of $27$ inches. To the nearest tenth of an inch, determine the length of the arc, $x$ , subtended by an angle of $1$ . $2$ radians. $\newline$ Answer: $\square$ inches

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Circles: word problems

Full solution

Q. Circle

O

shown below has a radius of

27

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

x

, subtended by an angle of

1

.

2

radians.

\newline

Answer:

\square

inches

Identify formula: Identify the formula to calculate the length of an arc in a circle. $\newline$ The length of an arc $L$ in a circle is given by the formula $L = r \times \theta$ , where $r$ is the radius of the circle and $\theta$ is the central angle in radians.
Plug values: Plug the given values into the formula. $\newline$ We are given the radius $r = 27$ inches and the central angle $\theta = 1.2$ radians. So, $L = 27$ inches $* 1.2$ radians.
Perform multiplication: Perform the multiplication to find the length of the arc. $L = 27 \, \text{inches} \times 1.2 \, \text{radians} = 32.4 \, \text{inches}.$
Round result: Round the result to the nearest tenth of an inch as requested. $\newline$ The length of the arc, to the nearest tenth of an inch, is $32.4$ inches (since it is already at the tenth of an inch, no further rounding is needed).

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\newline

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\newline

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