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Q. 69

Expert-verifiedFound in: Page 479

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**A sector of a circle of radius 80 miles has an area of $\mathbf{1600}{\mathbf{\text{\hspace{0.17em}miles}}}^{\mathbf{2}}$. ****Find the central angle (in radians) of the sector.**

The central angle for the given radius and the circular area is $\frac{\mathbf{1}}{\mathbf{2}}$ **radian**.

Area $\text{A}=1600{\text{\hspace{0.17em}miles}}^{2}$ and the radius $r=80$ miles.

Use the formula of the circular area $\text{A}=\frac{1}{2}{r}^{2}\theta $.

Central angle $\theta =\frac{2A}{{r}^{2}}$

$\theta =2\times \frac{1600}{{80}^{2}}$

$\theta =\frac{1}{2}$ radian.

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