Answer:
We have a rectangular prism of measures:
(2 + 1/4)ft by 9ft by 4ft
Let's analyze each one of the statements:
a) The base is a square?
A square has the same length as the width, this prism would have a square base if at least two of the dimensions are equal, but we can see that are all different, so we can conclude that the base can not be a square.
b) The volume of the rectangular prism is 81 cubic feet?
The volume will be equal to the direct product of the 3 dimensions, then the volume is:
V = (2 + 1/4)ft*9ft*4ft = 81 ft^3
This statement is true.
c) The area of the base is 36 square feet.
We know the dimensions, but we do not know which ones describe the base.
In the usual notation, the first two measures will describe the base of the figure, and the third one is the height.
Then the area of the base is:
(2 + 1/4)ft*9ft = 20.25 ft^2
The area of the base is not 36 ft^2
d) if you doubled the height, the volume would be the same:
Of course if we double one of the dimensions the volume will change, but let's calculate this.
The original height is 4ft, if we double this, the new heights Is 2*4ft = 8ft
Then the new volume will be:
V = (2 + 1/4)ft*9ft*8ft = 162 ft^3
The volume changes.
