Question

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°

Answer 1

`\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

Answer 2

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.