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Circle
O shown below has an arc of length 29 inches subtended by an angle of 1.1 radians. Find the length of the radius,
x, to the nearest tenth of an inch.
Answer:
inches

Circle $O$ shown below has an arc of length $29$ inches subtended by an angle of $1$ . $1$ radians. Find the length of the radius, $x$ , to the nearest tenth of an inch. $\newline$ Answer: $\square$ inches

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Circles: word problems

Full solution

Q. Circle

O

shown below has an arc of length

29

inches subtended by an angle of

1

.

1

radians. Find the length of the radius,

x

, to the nearest tenth of an inch.

\newline

Answer:

\square

inches

Formula rearrangement: To find the radius of the circle, we can use the formula for the length of an arc, which is $arc \ length = radius \times angle$ in radians. We need to rearrange the formula to solve for the radius (x). $\newline$ So, the formula to find the radius is $radius = \frac{arc \ length}{angle}$ .
Plugging in values: Now we can plug in the values we have into the formula. The arc length is $29$ inches and the angle is $1$ . $1$ radians. $\newline$ $x = \frac{29 \ inches}{1.1 \ radians}$
Division calculation: Performing the division to find the radius, we get: $\newline$ $x = \frac{29}{1.1}$ $\newline$ $x = 26.363636...$ inches
Rounding result: We need to round the result to the nearest tenth of an inch. Rounding $26.363636\ldots$ to the nearest tenth gives us $26.4$ inches.

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