Given a rectangular prism with dimensions w = 3, l = 4, and h = 6. If you created a second rectangular prism with the length doubled but the height halved (and the width stays the same), which would be the relation of the second volume to the first volume?

Question

calculusxy · Answer

Find the volume of the original rectangular prism ($3 \times 4 \times 6$)

herpderp · Answer

Find the volume of the original prism (4 x 3 x 6), then double the length (4 x 2) and halve the height (6/2) and solve for the new prism (8 x 3 x 3). So the original volume is 72 un^3 and the new volume is also 72 un^3. Therefore their volumes are the same.

calculusxy · Answer

So basically I asked for you to find the volume of the original rectangular prism just so that we can use it for a comparison with the second rectangular prism's volume. 

The volume of the original rectangular prism would be ($3 \times 4 \times 6 = 72$). The second rectangular prism would have the following dimensions:
width = 3 
length = 4 x 2 ( `because length is doubled` ) = 8
height = 6 / 2 ( `because height is halved` ) = 3

Now we can multiply all of the dimensions of the second rectangular together: $3 \times 8 \times = 72$. 

The original one = 72 units cubed 
The second one = 72 units cubed 

The relation would be, in simple words, that they have the same volume.