# Math Problem

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This is kind of shy to admit to, but I can't figure out what this problem is to mean.

The area of one of a rectangular box is 120 square centimeters. The
area of another face of the box is 72 square centimeters. The area of the
top of the box is 160 square centimeters. What is the volume of the box?

Been a very long day, anyone want to help my tired mama-brain...

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This is kind of shy to admit to, but I can't figure out what this problem is to mean.

The area of one of a rectangular box is 120 square centimeters. The

area of another face of the box is 72 square centimeters. The area of the

top of the box is 160 square centimeters. What is the volume of the box?

Is there a word missing? Should it not be

"The area of one face of a rectangular box is 120 square centimeters..."?

Let L,w and h be the side lengths of the box. The volume is V=L*w*h.

We know:

Side 1: L*h=120

Side 2: W*h=72

Top: L*W=160

V= sqrt( (L*w*h)^2)=sqrt [ (L*h)*(W*h)*(L*W)]= sqrt (120*72*160)=1176 cm^3

Edited by regentrude
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The volume will be l*w*h. The area of one face will be l*h, the area of one face will be w*h, and the area of the top will be l*w. Is this enough?

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Is there a word missing? Should it not be

"The area of one face of a rectangular box is 120 square centimeters..."?

You know it didn't occur to me that that might have been a typo in the original problem and not in how it was typed into the forum. I can totally see how that would be super confusing as well.

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This is not a well designed problem. If this were a good problem, the numbers would be so that the answer comes out a perfect cube square (fixed typo) so that students could solve it by prime factoring or identifying the three side lengths from the areas, instead of having to use a calculator. They would learn so much more... (all it would take is changing one digit and making it 12 instead of 72).

Who writes these???

Edited by regentrude
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This is not a well designed problem. If this were a good problem, the numbers would be so that the answer comes out a perfect cube so that students could solve it by prime factoring or identifying the three side lengths from the areas, instead of having to use a calculator. They would learn so much more... (all it would take is changing one digit and making it 12 instead of 72).

Who writes these???

I guess I had solved it by identifying the sidelengths.

I got h = 3 sqrt 6, w = 4 sqrt 6, l = 40/sqrt 6, then V = 480 sqrt 6 which agrees with your answer after use of a calculator at the last step.

My guess is that the question writer wanted to force them to use simultaneous equations and square roots as well???

Edited by kiana
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I guess I had solved it by identifying the sidelengths.

I got h = 3 sqrt 6, w = 4 sqrt 6, l = 40/sqrt 6, then V = 480 sqrt 6 which agrees with your answer after use of a calculator at the last step.

My guess is that the question writer wanted to force them to use simultaneous equations and square roots as well???

Oh yes, that would work too, of course.

I think it maybe depends on the grade level for which this question is intended.

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This question is from Math in Focus Course 1 (grade 6) , YET  I prepared the lesson in advance by some weeks and I made a mistake when I copied it out and did not know. I did not realize it until now. Thank you. The question truly reads:

The area of one face of a rectangular box is 120 square centimeters. The
area of another face of the box is 72 square centimeters. The area of the
top of the box is 60 square centimeters. What is the volume of the box?

Sorry to trouble all, I'm just to tired these days. My son became very frustrated with this problem and we kept working it.

My son will be so wroth with me when I tell him. Oopsie.

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