Answer:
The volume of prism A is the same as the volume of prism B.
Step-by-step explanation:
Given
See attachment for prisms
Required
Compare the volume of both
First, we calculate the volume of both prisms.
Prism A is a rectangular prism.
So, its volume is:
[tex]V_A = Length * Base * Height[/tex]
Where
[tex]Length \to a[/tex]
[tex]Base \to b[/tex]
[tex]Height \to h[/tex]
So:
[tex]V_A = abh[/tex]
For Prism B, we have:
[tex]Volume = Base\ Area * Height[/tex]
Where
[tex]Base\ Area = Length * Base[/tex]
and
[tex]Length = a[/tex]
[tex]Base = b[/tex]
So:
[tex]Base\ Area = a * b[/tex]
[tex]Base\ Area = a b[/tex]
The volume is then calculated as:
[tex]Volume = Base\ Area * Height[/tex]
[tex]V_B = ab * Height[/tex]
Where
[tex]Height \to h[/tex]
So:
[tex]V_B = ab * h[/tex]
[tex]V_B = abh[/tex]
By comparison:
[tex]V_A = V_B = abh[/tex]
