Find the length of each arc described. The length is a fractional
part of the circumference.)
An arc that is of the circumference of a circle with radius 12
An arc that has a measure of 270 and is part of a circle with
radius 12

Question

Find the length of each arc described. The length is a fractional
part of the circumference.)
An arc that is

of the circumference of a circle with radius 12
An arc that has a measure of 270 and is part of a circle with
radius 12

UpStudy AI · Accepted Answer

**Step 1. Calculate the circumference of a circle with radius 12**

The circumference $$ C $$ of a circle is given by  
$$
C = 2\pi r
$$  
Substitute $$ r = 12 $$:  
$$
C = 2\pi (12) = 24\pi
$$

**Step 2. Arc that is $$\frac{5}{8}$$ of the circumference**

The arc length $$ s_1 $$ is:  
$$
s_1 = \frac{5}{8} \times C = \frac{5}{8} \times 24\pi
$$  
Simplify the expression:  
$$
s_1 = \frac{5 \times 24\pi}{8} = \frac{120\pi}{8} = 15\pi
$$

**Step 3. Arc with a measure of 270° in a circle with radius 12**

First, express 270° as a fraction of the full circle:
$$
\text{Fraction} = \frac{270}{360} = \frac{3}{4}
$$  
The arc length $$ s_2 $$ is:  
$$
s_2 = \frac{3}{4} \times C = \frac{3}{4} \times 24\pi
$$  
Simplify the expression:  
$$
s_2 = \frac{3 \times 24\pi}{4} = \frac{72\pi}{4} = 18\pi
$$

**Final Answers:**

- The arc length that is $$\frac{5}{8}$$ of the circumference is $$15\pi$$.
- The arc length that measures 270° is $$18\pi$$.
The first arc is $$15\pi$$ units long, and the second arc is $$18\pi$$ units long.

Find the length of each arc described. The length is a fractional
part of the circumference.)
An arc that is of the circumference of a circle with radius 12
An arc that has a measure of 270 and is part of a circle with
radius 12

Upstudy AI Solution

Answer

Solution

Beyond the Answer

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Latest Geometry Questions

Find the length of each arc described. The length is a fractional part of the circumference.) An arc that is of the circumference of a circle with radius 12 An arc that has a measure of 270 and is part of a circle with radius 12

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Geometry Questions

Find the length of each arc described. The length is a fractional
part of the circumference.)
An arc that is of the circumference of a circle with radius 12
An arc that has a measure of 270 and is part of a circle with
radius 12