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Susan Athena
Susan Athena, Professional w/Adv. Degree
Category: Homework
Satisfied Customers: 4332
Experience:  10+ yrs teaching & tutoring. AP essay grader. 2 masters degrees. English, IT, business.
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Need some help figuring out something.. Im supposed to calculate

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Need some help figuring out something.. I'm supposed to calculate the volume of clay to be used to fill up this racetrack [shown here: http://i50.tinypic.com/2h2qc92.png] with 70cm of clay. rWidth is 300m, rLength is 400m, tWidth is 20m.

What I'm asking for is NOT an answer, but rather, the formula I'd need to use to find the volume. Any help would be appreciated, thank you. I've been at this for a while with no success.
Hi. Thanks for your question! It's an interesting problem. Here's how I'd solve it.

Start by calculating the area of the racetrack.

The racetrack is made up of two "strips" (the straight part of the track, along the top and bottom), plus a hollow circle. The circle is cut in half and stuck onto the two ends of the track.

So, first you calculate the area of the strips. Each strip has area tWidth * rLength, but you have to multiply that by two (because there are two of them) to get the Total Strip Area.


Now you need the area of the hollow circle. To get that, you first calculate the area of the outer circle. That's pi * r^2, where r is the radius of the circle.

The radius of the outer circle is half of rWidth + tWidth (basically, half the length of the dotted line in your diagram).


Then calculate the area of the inner circle. The formula is the same, but now the radius is half of rWidth only.

Area of the circular part of the track is Outer Circle Area - Inner Circle Area.

Now add the area of the circular part of the track to theTotal Strip Area and you've got the total racetrack area.

Once you have the area of the racetrack, calculate the volume by multiplying the area in meters by 0.7m (70cm) to get the area in m^3.

Let me know if you run into any trouble and I'd be happy to walk you through the steps in more detail. I think the hardest part of this is realizing that the two curved ends of the track make up a circle, and also how to find the radius of both the inner and outer circles.

Kind regards,
Susan
Customer: replied 4 years ago.

Hi Susan, I have a problem. When I ran the numbers I got 18017.25605, but the given answer says 25274.335088. Did I do something wrong or is there an error in the answer given to me? Thanks.

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Customer: replied 4 years ago.

Ah, I found it. Thanks for your help.

No worries. Feel free to ask for me anytime!