Question

PLEASE HELP

it can be answered in fraction form so please try that first

The circle below has center O, and its radius is 7 m. Given that m ZAOB= 150°, find the length of the arc ADB and the area of the shaded region.
Give exact answers in terms of , and be sure to include the correct units in your answer.

Answer 1

• 49π/6 m
• 343π/12 m²

Explanation:

Given a circle of radius 7 m with central angle AOB = 150°, you want the length of long arc AB and the area of the sector it bounds.

Arc length

The length of an arc of a circle is ...

s = rθ

where θ is the central angle in radians.

Here, the long arc in degrees is 360° -150° = 210°. In radians, that is ...

210° = 210°×π/180° radians = 7π/6 radians

So, the arc length is ...

s = (7 m)(7π/6) = 49π/6 m . . . . arc length

Area

The area of the sector is half the product of the arc length and the radius; (You can think of it as a kind of triangle.)

A = 1/2s·r

A = 1/2(49π/6 m)(7 m) = 343π/12 m² . . . . area