Question

Can someone help me answer 7, 8, and 9. Thank you!
I don’t really get the circle concept

Answer 1

Part 7) Option C. The approximate perimeter of the patio is
`54\ ft`

Part 8) Option G.
`3\ floats`

Part 9)
`150.72\ minutes`

Explanation:

Part 7) we know that

The perimeter of the figure is equal to the circumference of the larger half circle plus the circumference of the smaller half circle plus two times the length of 8 ft

step 1

Find the circumference of the larger half circle

The circumference of the larger half circle is

`C=\pi r`

we have

`r=8+2=10\ ft`

substitute

`C=\pi(10)`

`C=10\pi\ ft`

step 2

Find the circumference of the smaller half circle

The circumference of the smaller half circle is

`C=\pi r`

we have

`r=2\ ft`

substitute

`C=\pi(2)`

`C=2\pi\ ft`

step 3

Find the perimeter of the figure

`10\pi\ ft+2\pi\ ft+2(8)\ ft=(12\pi+16)\ ft`

assume
`\pi=3.14`

so

`(12(3.14)+16)=53.68=54\ ft`

Part 8) we know tat

The area of a circle is equal to

`A=\pi r^(2)`

we have

`A=28.26\ ft^(2)`

assume
`\pi=3.14`

substitute the values and solve for r

`28.26=(3.14)r^(2)`

`r^(2)=28.26/(3.14)`

`r^(2)=9`

`r=3\ ft`

Find the diameter D

`D=2r=2(3)=6\ ft`

Divide the width of the pool by the diameter of the floats

so

`(18)/(6)=3\ floats`

Part 9)

step 1

Find the circumference of one coaster

The circumference of circle is

`C=2\pi r`

we have

`r=1.5\ in`

assume
`\pi=3.14`

substitute

`C=2(3.14)(1.5)=9.42\ in`

step 2

Find the circumference of 48 coasters

so

`48(9.42)=452.16\ in`

step 3

we know that

The laser cut woods at the rate of 3 inches per minute

By proportion find how many minutes will it take to cut out 48 coasters

`(3)/(1)(inches)/(minute) =(452.16)/(x)(inches)/(minutes)\\ \\x=452.16/3\\ \\x=150.72\ minutes`