Question

although she's only in Tameka loves to drive go-carts. her favorite place to drive go carts is driver's delight has three circular tracks track one has a radius of 60 feet. Track two has a radius of 85 feet. track three has a radius of 110 feeta. compute the circumference of track 1b. compute the circumference of track 2.c. compute the circumference of track 3. d.driver's delight is considering building a new track. they have a circular space with a diameter of 150 ft. compute the circumference of the circular space.2. Tameka wants to build a circular go-kart track in her yard. a. if she wants the track to have a circumference of 150 ft what does the radius of the track need to be?b. if she wants to try to have a circumference of 200 feet, what does the radius of the track need to be?c. if she wants to have a circumference of 400 ft what does a diameter of the track need to be?

Answer 1

The circumference C of a circle of radius r is given by:

`C=2\pi r`

a)

Substitute r=60 feet to find the circumference of the first track:

`\begin{gathered} C_1=2\pi(60\text{feet)} \\ =120\pi\text{ feet} \\ =376.9911184\ldots\approx377\text{ feet} \end{gathered}`

b) Use the same procedure as in problem a), but substitute r=85 feet.

c) Use the same procedure as in problem a), but substitute r=110 feet.

d)

Since the diameter of a circle is twice its radius, then the circumference C is given in terms of the diameter D by the following equation:

`C=\pi D`

Substitute D=150 ft to find the value of the circumference.

Problem 2

a) Using the equation that relates the circumference in terms of the radius:

`C=2\pi r`

Divide both sides by 2*pi to isolate r:

`r=(C)/(2\pi)`

Substitute C=150ft to find out the value of r:

`r=(150ft)/(2\pi)=23.87324146\approx23.87`

b) Use the same procedure as in part a) but substitute C=200ft.

c) This question asks for the diameter instead of the radius. Use the equation:

`C=\pi D`

Divide both sides by pi to isolate D:

`D=(C)/(\pi)`

And then substitute C=400 ft. You may also find the radius first and then multiply by 2 to find the diameter, since:

`D=2r`