Question

A rectangular prism had a volume of 252 cubic centimeters. The length of the prism is 14 centimeters and the width of the prism is 6 centimeters. The height of the prism was changed from 3 centimeters to 6 centimeters to create a new rectangular prism. The other dimensions stayed the same. What do you know about the volume of the new prism

Answer 1

A prism is a solid object having two identical bases, hence the same cross section along the length. Prism are called after the name of their base. A rectangular prism is a solid whose base is a rectangle. Multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:

`V=L* W* H`

FOR THE ORIGINAL PRISM WE HAVE THE FOLLOWING DIMENSIONS:

`L=14cm \\ \\ W=6cm \\ \\ H=3cm`

In fact, the volume is
`252cm^3` because:

`V=14* 6* 3 \therefore V=252cm^3`

Now the height of the prism was changed from 3 centimeters to 6 centimeters to create a new rectangular prism, therefore:

FOR THE NEW PRISM WE HAVE THE FOLLOWING DIMENSIONS:

`L=14cm \\ \\ W=6cm \\ \\ H=6cm`

So the new volume is:

`V=14* 6* 6 \therefore V=504cm^3`

What do we know about the volume of the new prism?

Well, the volume has increased from
`252cm^3 \ to \ 504cm^3` and since
`504=2* 252` we can say that the new volume is two times the original volume.