Question

A display case for the artifact is in the shape of a cube. Each side of the display case is three times longer than the width ww of the artifact. a. Write an expression for the volume of the case. Write your answer as a power. Written as a power, an expression for the volume is . b. Simplify the expression. A simplified expression for the volume is .

Answer 1

A cube is a 3d object bounded by  6 square faces. 

Each side of the display case is 3 times longer than the width of the artifact.

width of the artifact = w
side of the cube = 3w

a. Write an expression for the volume of the case.
 volume of a cube is the measure of its side raised to the power of 3.

Volume = (3w)³

Volume = 27w³

Answer 2

An expression for the volume of the cubic display case that is three times longer than the width of the artefact is 27a³.

Let us say the size of the artefact =a

So, the side of the display case = 3a

What is the volume of a cube?

The volume of a cube with side a is a³.

So, the volume of the display case = (3a)³

The volume of the display case = 27a³.

Thus, an expression for the volume of the display case is 27a³.

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