Everyone can answer this. You can get the best answer just by getting this easy math problem correct. Easy!!!!

Question

The city of New York is discussing the idea of building a new race track downtown. The track would be circular, with the width of the track being 30 ft. If the circumference of the outside wall of the track is 502.4 ft., and it costs $20 per square foot of concrete, how much would the concrete cost the city?


Please show your work and explain how you got your answer.
This should be an easy problem for you, you can get the best answer just by getting the correct answer! It's easy!!

Answer 1

Method to solve this:

The circumference is 502.4 ft. Using the formula for circumference (C = 2π R), you can easily figure out the outer radius R.

Hint: Divide by 2π.

Subtract 30 to get the inner radius r.

Hint: using 3.14 as an estimate for pi, you should get a round number for R and r ---> a multiple of 10 in both cases...

Now you have two circles. Take the area of the larger circle (Area1 = π R²) and subtract the area of the smaller circle (Area2 = π r²).

So the area of just the track will be:
π (R² - r²)

Hint: The answer is between 12,000 and 13,000 sq. ft.

Multiply that by $20 per square foot to get the cost of the concrete.

Hint: The final answer is close to $250,000. If you add up the digits in the final answer the sum is 21...

I could do this all for you, but I think it will make more sense if you do it yourself. If you need more help on any of the steps, though, just post back with a follow-up note.

Answer 2

Basically, you have two concentric circles like in a dough nut. Find the area of the outer circle and subtract the area of the inner circle. This will give you the area of the dough nut, then we can multiply that by $20 to find the total cost.

First to find the Area of the outer circle:
A = pi*r^2

but they didn't give you radius, they did however tell you the perimeter of the large circle is 502.4 ft. P = pi*d or P = pi*2r (since 2 times the radius is the diameter). Now using P = pi*2r, lets find the radius:

Substitute:502.4=pi* 2r
Divide both sides by 2: 2512 = pi*r
Divide both sides by pi: r=79.96 (lets round and say r = 80 ft)

Now we can use A = pi*r^2 to find the area of the larger circle:
Substitute for the radius: A = pi*80^2
Solve and round: A of large circle = 20106 sq ft

Now to find the area of the smaller circle, we need to know the radius of the large circle - 30 ft is the radius of the smaller circle, that means that 80-30 = r of small circle = 50

Now we can use A = pi*r^2 to find the area of the smaller circle:
Substitute for the radius: A = pi*50^2
Solve and round: A of small circle = 7854 sq ft

So the area of the track is 20106 - 7854 = 12252 sq ft.

Multiply the area times the cost per square foot to get the total cost:
T = 12252 * 20


T = $245,040

Answer 3

The answer is track square footage x $20.

Track square footage is the area of a circle with circumference 502.4 less the area of a circle with radius 30 feet less than the larger.

Circumference = pi * Diameter
Diameter = 2 * radius, radius=Diameter/2
Circle Area = pi * r^2

Say larger circle is C1 and smaller (inner) circle is C2.

C1 given as 502.4
C1 = pi * D1 =502.4, thus D1 = 502.4/pi = 159.92 feet
Area C1 = pi*(159.92/2)^2 = pi * 6393.6 = 20,086 sq ft

D2=159.92-30 = 129.92
R2=129.92/2 = 64.96
Area C2 = pi * 64.96^2 = pi * 4219.8 = 13,256 sq ft

Area C1 - Area C2 = 20,086 - 13,256 = 6,830 sq ft

Cost = 6,830 * $20 = $136,600

Answer 4

Big radius = 502.4/(2pi) = 80 ft

smaller radius = 80 - 30 = 50ft

track area = (80^2 - 50^2)pi = 12246 sqft
cost = 20 * 12246=244920 $

Answer 5

(3.14)(d)=501.4
diameter whole circle=159.68
radius whole circle=79.84
diameter of center (no track)=159.68-30=129.68
radius of center (no track)=64.84
area whole circle=79.84(79.84)(3.14)=20015.7
radius of center (no track)=64.84(64.84)(3.14)=13201.3
area of track =20015.7-13201.3=6814.4 sq ft
6814.4 sq ft*$20 sq ft=$136288.63
This assumes no thickness of concrete, which of course if impossible. I think concrete is sold by the cubic foot so in reality this should be a volume problem with the thickness of the concrete (4 to 6 inches) provided.

Answer 6

Divide 30 by 2 to get 15(which is the radius)
Times 15 by 15 to get 225
Time 225 by 3.14 to 706.5 sq. ft.
Times 706.5 by 20 to get $14,130

Hope I'm right!

Answer 7

2(pi)r = 502.4 ft => r = 502.4/2(3.142) ft = 80 ft
inner radius i = r -- 30 ft = 50 ft
area = pi(r^2 -- i^2) = 3.142(r+i)(r--i) = 3.142(130)(30) = 12254 ft^2
cost = area*rate = 12254*$20 = $245080