Question

The concentric circles
`(x-3)^2+(y-5)^2=64` and
`(x-3)^2+(y-5)^2=25` form a ring. The lines
`y=(2)/(3) x+3` and
`y=5` intersect the ring, making four sections. Find the area of each section. Round your answers to the nearest tenth of a square unit.

Answer 1

11.5 square unit, 11.5 square wnit
49.8 squave unit, 49.8 square unit

Explanation:

`When\ x=3,y=(2)/(3)*3+3=5.`

`tan(\theta)=(2)/(3)\Rightarrow{\theta}=33.69\ degrees`

`A_1=\pi(R^2-r^2)\bullet(33.69\ degrees)/(360\ degrees)\\ =\pi(64-25)\bullet(33.69\ degrees)/(360\ degrees)\\ =11.5`

`A_2=\pi(R^2-r^2)\bullet(180\ degrees-33.69\ degrees)/(360\ degrees)\\ =\pi(64-25)\bullet(146.31\ degrees)/(360\ degrees)=49.8`

`A_3=A_1=11.5\\ A_4=A_2=49.8`

`elementany\ calculation`

I hope this helps you

:)

Answer 2

Hi,

Please check the attached picture of the explanation...

Thank you!