QuestionCalculate the arc length of a circle with radius 12 inches and central angle $\frac{3}{4} \pi$ radians. Round to two decimals.

Studdy Solution

STEP 1

Assumptions1. The radius of the circle is12 inches. . The central angle measures $\frac{3}{4} \pi$ radians.
3. We are to find the arc length of the circle.

STEP 2

The formula to find the arc length () of a circle is given by $= r \cdot \theta$ where r is the radius of the circle and $\theta$ is the central angle in radians.

STEP 3

Now, plug in the given values for the radius and the central angle to calculate the arc length.
$=12 \, inches \cdot \frac{3}{} \pi \, radians$

STEP 4

Perform the multiplication to calculate the arc length.
$=12 \, inches \cdot \frac{3}{4} \pi \, radians =9\pi \, inches$

STEP 5

Now, we need to convert the result into a decimal and round to the nearest hundredth.
$\approx9\pi \, inches \approx28.27 \, inches$ So, the arc length of the circle is approximately28.27 inches.

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QuestionCalculate the arc length of a circle with radius 12 inches and central angle $\frac{3}{4} \pi$ radians. Round to two decimals.

Studdy Solution

STEP 1

Assumptions1. The radius of the circle is12 inches. . The central angle measures $\frac{3}{4} \pi$ radians.
3. We are to find the arc length of the circle.

STEP 2

The formula to find the arc length () of a circle is given by $= r \cdot \theta$ where r is the radius of the circle and $\theta$ is the central angle in radians.

STEP 3

Now, plug in the given values for the radius and the central angle to calculate the arc length.
$=12 \, inches \cdot \frac{3}{} \pi \, radians$

STEP 4

Perform the multiplication to calculate the arc length.
$=12 \, inches \cdot \frac{3}{4} \pi \, radians =9\pi \, inches$

STEP 5

Now, we need to convert the result into a decimal and round to the nearest hundredth.
$\approx9\pi \, inches \approx28.27 \, inches$ So, the arc length of the circle is approximately28.27 inches.

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QuestionCalculate the arc length of a circle with radius 12 inches and central angle 34π\frac{3}{4} \pi43​π radians. Round to two decimals.

Studdy Solution

STEP 1

Assumptions1. The radius of the circle is12 inches. . The central angle measures 34π\frac{3}{4} \pi43​π radians.3. We are to find the arc length of the circle.

STEP 2

The formula to find the arc length () of a circle is given by=r⋅θ = r \cdot \theta=r⋅θwhere r is the radius of the circle and θ\thetaθ is the central angle in radians.

STEP 3

Now, plug in the given values for the radius and the central angle to calculate the arc length.=12 inches⋅3π radians =12 \, inches \cdot \frac{3}{} \pi \, radians=12inches⋅3​πradians

STEP 4

Perform the multiplication to calculate the arc length.=12 inches⋅34π radians=9π inches =12 \, inches \cdot \frac{3}{4} \pi \, radians =9\pi \, inches=12inches⋅43​πradians=9πinches

STEP 5

Now, we need to convert the result into a decimal and round to the nearest hundredth.≈9π inches≈28.27 inches \approx9\pi \, inches \approx28.27 \, inches≈9πinches≈28.27inchesSo, the arc length of the circle is approximately28.27 inches.

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QuestionCalculate the arc length of a circle with radius 12 inches and central angle $\frac{3}{4} \pi$ radians. Round to two decimals.

Assumptions1. The radius of the circle is12 inches. . The central angle measures $\frac{3}{4} \pi$ radians.
3. We are to find the arc length of the circle.

The formula to find the arc length () of a circle is given by $= r \cdot \theta$ where r is the radius of the circle and $\theta$ is the central angle in radians.

Now, plug in the given values for the radius and the central angle to calculate the arc length.
$=12 \, inches \cdot \frac{3}{} \pi \, radians$

Perform the multiplication to calculate the arc length.
$=12 \, inches \cdot \frac{3}{4} \pi \, radians =9\pi \, inches$

Now, we need to convert the result into a decimal and round to the nearest hundredth.
$\approx9\pi \, inches \approx28.27 \, inches$ So, the arc length of the circle is approximately28.27 inches.