Converting sq.in. to cubic in.

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Converting sq.in. to cubic in.

Postby HeatherDiBasco » Thu Mar 31, 2005 11:09 am

I'm having trouble with a math problem. The problem reads:

The area of the top of a rectangular box is 324 sq.in., the area of the front of the box is 135 sq.in., and the area of the end is 60 sq.in. What is the volume of the box?

I know I need to convert from sq.in. to cubic inches to answer the question but how? Area does not equal volume, and if I multiply all the areas, I get inches^6. How would I convert this?

Any help is appreciated!!
HeatherDiBasco
 

Postby Guest » Thu Mar 31, 2005 6:42 pm

It's really an algebra problem, not a conversion problem. If the three dimensions are l, w, h, then:
1) l*w = 324
2) l*h = 135
3) w*h = 60

I was going to suggest solving the three equations for the three unknowns but just saw a simpler way.

If I multiply the three equations together, I get
l^2 x h^2 x w^2 = 324 x 135 x 60
The lefthand side is (l*w*h)^2 or volume squared,
so V = sqrt(324x135x60) = 1620 cu in.

If you need the dimensions as well as the volume, try variations of this:
Multiplying eqs 2 & 3
l*w*(h^2) = 135 x 60 but l*w = 324 so
324*(h^2) = 135 x 60 and you can solve for h.
Similar substitutions will give l and w.
Guest
 

Postby Guest » Thu Mar 31, 2005 6:42 pm

It's really an algebra problem, not a conversion problem. If the three dimensions are l, w, h, then:
1) l*w = 324
2) l*h = 135
3) w*h = 60

I was going to suggest solving the three equations for the three unknowns but just saw a simpler way.

If I multiply the three equations together, I get
l^2 x h^2 x w^2 = 324 x 135 x 60
The lefthand side is (l*w*h)^2 or volume squared,
so V = sqrt(324x135x60) = 1620 cu in.

If you need the dimensions as well as the volume, try variations of this:
Multiplying eqs 2 & 3
l*w*(h^2) = 135 x 60 but l*w = 324 so
324*(h^2) = 135 x 60 and you can solve for h.
Similar substitutions will give l and w.
Guest
 

Re: Converting sq.in. to cubic in.

Postby Guest » Thu Mar 23, 2006 7:42 am

HeatherDiBasco wrote:I'm having trouble with a math problem. The problem reads:

The area of the top of a rectangular box is 324 sq.in., the area of the front of the box is 135 sq.in., and the area of the end is 60 sq.in. What is the volume of the box?

I know I need to convert from sq.in. to cubic inches to answer the question but how? Area does not equal volume, and if I multiply all the areas, I get inches^6. How would I convert this?

Any help is appreciated!!
Guest
 


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