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The figure below shows a container that is a square prism with base side length B and a hollow section (shaded region) that is a square prism with base side length 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.

The figure below shows a container that is a square prism with base side length B-example-1
User Soverman
by
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1 Answer

3 votes

we know that

The volume of a square prism is equal to


V=A*H

where

A is the area of the base of the prism

H is the height of the prism

The volume of the container is equal to the volume of the larger prism minus the volume of the smaller prism

Step 1

Find the volume of the larger prism


V=A*H

In this case


A=B^(2)\ units^(2)


H=h\ units


V=B^(2)*h\ units^(3)

Step 2

Find the volume of the smaller prism


V=A*H

In this case


A=b^(2)\ units^(2)


H=h\ units


V=b^(2)*h\ units^(3)

Step 3

Find the volume of the container

The volume of the container is equal to the volume of the larger prism minus the volume of the smaller prism

so


V=(B^(2)*h)\ units^(3)-(b^(2)*h)\ units^(3)

Simplify


V=[B^(2)-b^(2)]*h\ units^(3)

Difference of squares


V=[B-b]*[B+b]*h\ units^(3)

therefore

the answer is


V=[B-b]*[B+b]*h\ units^(3)


User Trafalmadorian
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