## Converting sq.in. to cubic in.

Questions and answers on how to convert things from one unit or system to another
Forum rules
Dear convert-me.com forum visitors,

Our forum has been available for many years. In September 2014 we decided to switch it to read-only mode. Month after month we saw less posts with questions and answers from real people and more spam posts. We were spending more and more resources cleaning the spam until there were less them 1 legitimate message per 100 spam posts. Then we decided it's time to stop.

All the posts in the forum will be available and searchable. We understand there are a lot of useful information and we aren't going to remove anything. As for the new questions, you can always ask them on convert-me.com FaceBook page

Thank you for being with us and sorry for any inconveniences this could caused.

### Converting sq.in. to cubic in.

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

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

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.

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