Question

Which statement best compares the volumes of the two rectangular prisms

Answer 1

The volume of prism A is the same as the volume of prism B.

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:

`V_A = Length * Base * Height`

Where

`Length \to a`

`Base \to b`

`Height \to h`

So:

`V_A = abh`

For Prism B, we have:

`Volume = Base\ Area * Height`

Where

`Base\ Area = Length * Base`

and

`Length = a`

`Base = b`

So:

`Base\ Area = a * b`

`Base\ Area = a b`

The volume is then calculated as:

`Volume = Base\ Area * Height`

`V_B = ab * Height`

Where

`Height \to h`

So:

`V_B = ab * h`

`V_B = abh`

By comparison:

`V_A = V_B = abh`