Question

A right rectangular prism has base dimensions of 3 inches by 12 inches and a height of 5 inches. An oblique rectangular prism has base dimensions of 4 inches by 9 inches and a height of 5 inches. Are the volumes the same?

Answer 1

B. The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.

Explanation:

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Answer 2

Yes they are. Given that a volume of a rectangular prism is V=l•w•h, we can plug them into an equation and compare them. I'll call the Right rectangular prism figure R and the oblique rectangular prism O


For Figure R, We know all the basic needs to find the volume. This means we can plug it in.

V=l•w•h
V=12•3•5
Now We can solve for V
V=12•15
V=180

The volume of the right rectangular prism is 180in^3


Now, For figure O.
V=9•4•5
V=9•20
V= 180.


With this in mind, We now can say that the volumes of both the rectangular prisms are the same.