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How do I find the volume of the box?

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1 Answer 1

up vote 4 down vote accepted

Volume = (area of base) $\times$ height.

Volume needed/given (old box with base dimensions $2\times 6$, and height $h = 10$):

$V = (2 \times 6) \times 10 = 120\;$ cubic inches.

Now, you want a new a box with a base area of $\;b = (3 \times 5) = 15\;$ squared inches, and need to find height, while keeping the volume of $120$ cubic inches constant:

Again, as given, Volume is $\;V$ = (area of base) $\times $ height $(h)$, i.e. $\;\;V = b\times h$

We know $V$ and we know $b$, so we plug those values in and solve for $h$, height of new box.

$$V = 120 = 15 \times h \quad\implies\quad h = 120/15 = 8 \text{ inches}$$

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Many thanks again! –  Little Jon Feb 15 '13 at 22:25
    
You're welcome, Little Jon! –  amWhy Feb 15 '13 at 22:25
    
It looks like a school problem! isn't it? + –  Babak S. Feb 16 '13 at 6:25

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