11. Find the length of the arc on a circle of radius r intercepted by a central angle Theta Round answer to two decimal places . (Take pi =3.14 ) Do not use a calculator. r=15inches,Theta =210^circ square

To find the length of the arc on a circle of radius \( r \) intercepted by a central angle \( \Theta \), we can use the formula:<br /><br />\[ \text{Arc length} = \frac{\Theta}{360^\circ} \times 2\pi r \]<br /><br />Given:<br />- \( r = 15 \) inches<br />- \( \Theta = 210^\circ \)<br />- \( \pi = 3.14 \)<br /><br />First, substitute the given values into the formula:<br /><br />\[ \text{Arc length} = \frac{210^\circ}{360^\circ} \times 2 \times 3.14 \times 15 \]<br /><br />Next, simplify the fraction:<br /><br />\[ \frac{210}{360} = \frac{7}{12} \]<br /><br />Now, substitute this back into the formula:<br /><br />\[ \text{Arc length} = \frac{7}{12} \times 2 \times 3.14 \times 15 \]<br /><br />Calculate the multiplication step-by-step:<br /><br />\[ \frac{7}{12} \times 2 = \frac{14}{12} = \frac{7}{6} \]<br /><br />Then,<br /><br />\[ \frac{7}{6} \times 3.14 = \frac{21.98}{6} \]<br /><br />Finally,<br /><br />\[ \frac{21.98}{6} \times 15 = 35.9833 \]<br /><br />Rounding to two decimal places:<br /><br />\[ \text{Arc length} \approx 35.98 \text{ inches} \]<br /><br />So, the length of the arc is approximately \( 35.98 \) inches.