Volume

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JulianMathHelp

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I did this volume problem involving a equilateral triangle prism with all edges length 2 inches. I was supposed to find the volume of the given prism, and then find the weight of the prism with the given conversion (19.3gm/cc). I got a different answer from my teacher's but I checked all my work and it seems correct.

Given conversions my teacher gave: (in = 2.54cm) (cm = 0.394in)
My strategy was that I converted my dimensions from in to cm right away. Then, I found the area of a base (11.17449899 cm^2), and multiplied it by the height to get the volume which turned out to be 56.76645487 cm^3. Then, I converted it to grams which turned out to be (~1095.59gm)

My teacher's strategy was that she did not convert the dimensions right away, but found the area of the base first (root3 in), and multipled it by the height to get the volume (2root3 in^3). Then, she converted it into cm using (cm=0.394in)^3 conversion, and got the answer for the volume to be 56.63722383 cm^3. Then she converted it to rams which turned out to be around 1093 gm.

I don't see my mistake. What is it?
 
Can you tell us/ show us your calculations rather than just the end results. Thank you.
 
The prism is a prism with lateral faces as rectangles and the bases are equilateral triangles. All the edges are 2in.
 
The small difference (of about 2.6 in 1095) was probably caused by a difference between the two conversion factors.

1/2.54 ≈ 0.3937 which is different to the 0.394 that your teacher used, probably enough to produce the difference in your figures. Judging by the top few Google results the 2.54 figure is most quoted, so it was your teacher's answer that was (slightly) wrong.
 
Cubist said:
The small difference (of about 2.6 in 1095) was probably caused by a difference between the two conversion factors.

1/2.54 ≈ 0.3937 which is different to the 0.394 that your teacher used, probably enough to produce the difference in your figures. Judging by the top few Google results the 2.54 figure is most quoted, so it was your teacher's answer that was (slightly) wrong.
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Thanks.
Jomo said:
What is the base and height in inches of triangle ABC
Click to expand...
I think it’s in my work.
 
Cubist said:
The small difference (of about 2.6 in 1095) was probably caused by a difference between the two conversion factors.

1/2.54 ≈ 0.3937 which is different to the 0.394 that your teacher used, probably enough to produce the difference in your figures. Judging by the top few Google results the 2.54 figure is most quoted, so it was your teacher's answer that was (slightly) wrong.
Click to expand...
So my way was shown more in google results?
 
JulianMathHelp said:
Thanks.

I think it’s in my work.
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True, but I am suggesting that it is wrong. For example the base is clearly 2 in which you converted to 5.08 cm which i s good. However in your formula for the area of triangle ABC I do not see 5.08cm. Nor do I see the correct height. You wrote that the area of triangle ABC is (1/2)(2.54*sqrt(3)/3)*(15.25)?? Where did those numbers come from????
 
Jomo said:
True, but I am suggesting that it is wrong. For example the base is clearly 2 in which you converted to 5.08 cm which i s good. However in your formula for the area of triangle ABC I do not see 5.08cm. Nor do I see the correct height. You wrote that the area of triangle ABC is (1/2)(2.54*sqrt(3)/3)*(15.25)?? Where did those numbers come from????
Click to expand...
I used a different formula, not sure why. It is 1/2(apothem)(perimeter). Only for regular polygons
 
JulianMathHelp said:
I used a different formula, not sure why. It is 1/2(apothem)(perimeter). Only for regular polygons
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OK, I get it now. Thanks.
If you are going to call something that area of a triangle then I will assume that you are computing the area of a triangle.
 
Jomo said:
OK, I get it now. Thanks.
If you are going to call something that area of a triangle then I will assume that you are computing the area of a triangle.
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I’m not sure I follow you. If I’m going to call something that area of a triangle?
 
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JulianMathHelp said:
So my way was shown more in google results?
Click to expand...
Just to be clear, I'm not saying that your method of solution showed up in any Google results. I'm referring only to the conversion factor in <=> cm which seems to be a very likely culprit for the difference in the answers.

I typed "inch to cm" and "cm to inch" into Google, and the number 2.54 showed up on both sets of results pages. I did not see 1cm=0.394inches anywhere. Most pages seemed to have a few more decimal places if they were converting in this direction, for example 1cm=0.393701in)

You could confirm that this accounts for the difference by repeating your calculation but this time use the other conversion factor. If you suddenly get the same answer as your teacher then we will know for sure.
 
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