Anthony is designing a circular ice skating rink. He wants to build the rink so that 12 laps around the outside rail will equal a distance of 1 mile. To the narest foot, what length should he use for the radius of the rink? (Hint: 1 mile = 5280ft)

Question

OronSH · Answer

Let r be the radius. Then, write an expression for the circumference of the circle. Use this to find out how much 12 laps would be in terms of r then set it equal to 1 mile.

jordanbenton · Answer

well for the radius I got 16587.60921

OronSH · Answer

What was your equation?

jordanbenton · Answer

5280 ÷ 2 = 2640 feet.

OronSH · Answer

first you need to find the circumference in terms of r, then multiply it by 12

jordanbenton · Answer

@jordanbenton wrote:

well for the radius I got 16587.60921

i made a mistake i got that for the circumference and for the radius i got 2640

OronSH · Answer

remember that the radius is r not 1 mile, so you should get that the circumference is 2*pi*r, so 12 laps would be 12 times that. You need to set 12*2*pi*r equal to 5280 feet

jordanbenton · Answer

i got 5204.601776 for the radius

OronSH · Answer

you need to solve the equation 24pi r=5280, do you know how to solve this?

jordanbenton · Answer

yes the answer is 5204.601776 or the radius is 5204.64

OronSH · Answer

that's not right, are you sure you divided it correctly?

jordanbenton · Answer

yes

OronSH · Answer

what did you put in your calculator?

jordanbenton · Answer

wait is the radius 4.9

OronSH · Answer

you should get that the radius is $\frac{5280}{24\pi}$

jordanbenton · Answer

the radius is 691.15038379

OronSH · Answer

remember that you need to put 24pi in parenthesis otherwise it would do 5280/24 multiplied by pi instead of 5280/(24pi)

jordanbenton · Answer

is the radius 70.0281749604

OronSH · Answer

yes, that's right! good job!

jordanbenton · Answer

thanks for your help

cuzican · Answer

@oronsh wrote:

yes, that's right! good job!

not even in this but that is a real thank u-