Question

Don't understand, please help

Answer 1

`\huge \boxed{\mathrm{a. \ 13.96 \ ft}} \\ \\ \\ \huge \boxed{\mathrm{b. \ 69.81 \ ft^2 }}`

`\rule[225]{225}{2}`

Explanation:

Arc length = θ/360 × 2πr

80/360 × 2π(10)

40/9π ≈ 13.96

Area of sector = θ/360 × πr²

80/360 × π(10)²

200/9π ≈ 69.81

`\rule[225]{225}{2}`

Answer 2

see below

Explanation:

s = r theta where r is the radius and theta is the central angle in radians

theta = 80 * pi/180 = 4 pi/9

PQ = 10 * 4 pi/9

= 40 pi/9 ft

To find the area of the sector, first find the area of the circle

A = pi r^2

= pi ( 10)^2

= 100 pi

The sector is 80/360 = 2/9 so the sector is 2/9 of the circle

Multiply the area by the fraction of the circle that the sector is

100 pi* 2/9 = 200 pi /9 ft^2