what are possible dimensions for a rectangular prism with a volume of 60 cubic feet?

Answer 1

Hi,

Volume = length x width x height, so any 3 positive values that multiply to 60 could be the dimensions.

So 3 feet x 4 feet x 5 feet would give 60 cubic feet

But 2 feet x 10 feet x 3 feet would also give 60 cubic feet

60 feet x 1 foot x 1 foot would give 60 cubic feet

300 feet x 1/3 foot x 3/5 foot would give 60 cubic feet



I hope that helps!! :-)

Answer 2

V=lwh, where l=length, w=width, and h = height.
So any combination of real numbers that satisfy the equation are possible solutions. If you restrict the values of l,w, and h to being integers, then some of the possible values :
l=12, w=5, h = 1
l=15, w=4, h=1
l=15, w =2, h=2
l=5, w =3, h=4
You of course can exchange values to get more combinationsof numbers.
You can also divide one of the dimensions by any number and multiply another dimension by the same number and thus you can arrive at an infinite number of combinations.

If you restrict l,w,and h to integers, then there is a limited number of combinations which you should be able to easily work out. However, no such restriction was given in the problem, so the answer is infinite.

Answer 3

60 Cubic Feet

Answer 4

I'm assuming that the prism is an equilateral triangle shape:

volume = ½ * base * height * length

height = ½ * base * √3

½ * base = height ÷ √3

So, substituting back into the original equation:

volume = height² * length ÷ √3

Since the volume is 60, then we have:

60 = height² * length ÷ √3

Solve for either variable to get it in terms of the other:

length = 60 * √3 ÷ height²