The figure below shows a container that is a square prism with base area B and a hollow section (shaded region) that is a square prism with base area b. If the height h of both prisms is the same, write an expression to represent the volume of the container. Express your answer in completely factored form.
Question
The figure below shows a container that is a square prism with base area B and a hollow section (shaded region) that is a square prism with base area b. If the height h of both prisms is the same, write an expression to represent the volume of the container. Express your answer in completely factored form.
Solution
The volume of a prism is given by the formula V = Bh, where B is the base area and h is the height.
For the given figure, the total volume of the container would be the volume of the larger square prism minus the volume of the smaller square prism (the hollow section).
The volume of the larger square prism is Bh and the volume of the smaller square prism is bh.
Therefore, the volume of the container is V = Bh - bh.
Factoring out the common factor h, we get V = h(B - b).
So, the volume of the container in completely factored form is h(B - b).
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