Is it possible for two right rectangular prisms to have the same volume yet not have the exact same dimensions? If it is not possible, explain why. If it is possible, give an example that proves the statement.
It sure is possible.
The volume of a rectangular prism, (a box), is
Length*Width*Height.
So all you need is 3 different numbers that have the same product.
one example of that is
4 by 12 by 5 which is 240 cubic units
8 by 3 by 10 which is 240 cubic units
omigosh thanks so much! I thought it was possibly but wasn't sure how to prove it. Now I know :)
what is the gcf of 75 and 40?
correct 0.0185 to 3 significant figures
Yes, it is possible for two right rectangular prisms to have the same volume but different dimensions.
To understand why this is possible, let's begin by looking at the formula for the volume of a rectangular prism:
Volume = length × width × height
For two prisms to have the same volume, their product of length, width, and height must be equal. This means that as long as the dimensions are such that the product remains the same, the volumes will also be the same.
Here's an example to illustrate this:
Prism 1:
Length = 6 units
Width = 3 units
Height = 2 units
Volume = 6 × 3 × 2 = 36 cubic units
Prism 2:
Length = 4 units
Width = 3 units
Height = 3 units
Volume = 4 × 3 × 3 = 36 cubic units
As you can see, even though the dimensions of Prism 1 and Prism 2 are different, their volumes are the same.
In general, as long as the product of the dimensions of two right rectangular prisms is the same, their volumes will also be the same. This property allows for different possible configurations of prisms with equal volumes.