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Circle O shown below has a radius of 9 inches. To the nearest tenth of an inch,

determine the length of the arc, x, subtended by an angle of 81°.
9 inches
10=81°

Circle O shown below has a radius of 9 inches. To the nearest tenth of an inch, determine-example-1

2 Answers

3 votes

Answer:


\boxed{12.7\;inches}

Explanation:

For a circle of radius r, the circumference is given by the expression

C = 2πr

So for this circle of radius 9", the circumference is 2 x π x9 = 18π

The entire circle covers a total angle of 360°

If there is a sector of the circle that is subtended by an angle Ф, then the length of that arc will be Ф/ 360 x C

Here Ф = 81°

So length of arc is


(81)/(360) * 18 \pi\\\\\\\textrm {Using a calculator this works out to }\\\\


(81)/(360) * 18 \pi = 12.72345\\\\

Rounded to the nearest tenth of an inch this would be

\boxed{12.7\;inches} ANSWER

User Babatunde Mustapha
by
8.0k points
3 votes

The length of the arc (x) subtended by an angle of 81° in a circle with a radius of 9 inches is approximately 12.7 inches.

To solve this problem

The length of an arc in a circle is given by the formula:

Arc Length = (Angle/360) * 2 * π * Radius

In this instance, the central angle is 81 degrees and the radius is specified as 9 inches. Changing these numbers in the formula:

Arc Length = (81/360) * 2 * π * 9

Now, calculate the arc length:

  • Arc Length ≈ (81/360) * 18π
  • Arc Length ≈ 4.05π

To find the approximate numerical value, multiply by π:

  • Arc Length ≈ 4.05 * 3.14
  • Arc Length ≈ 12.687 inches

Therefore, to the nearest tenth of an inch, the length of the arc (x) subtended by an angle of 81° in a circle with a radius of 9 inches is approximately 12.7 inches.

User Heetola
by
8.2k points
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