Question

find the length of arc abc. use 3.14 for the value of \\(\pi\\). round to the nearest hundredth of a cm.

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc is \( L=\frac{\theta}{360^\circ}\times2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

Step2: Identify values

Here, \( \theta = 90^\circ \) and \( r = 32 \) cm. We use \( \pi = 3.14 \).

Step3: Substitute into formula

Substitute the values into the formula: \( L=\frac{90^\circ}{360^\circ}\times2\times3.14\times32 \).
First, simplify \( \frac{90^\circ}{360^\circ}=\frac{1}{4} \). Then the formula becomes \( L=\frac{1}{4}\times2\times3.14\times32 \).
Calculate \( 2\times3.14 = 6.28 \), then \( \frac{1}{4}\times6.28\times32 \).
\( 6.28\times32 = 200.96 \), then \( \frac{1}{4}\times200.96 = 50.24 \).

Answer:

50.24