The volume of a cube is 64 cubic inches. Which expression represents [tex]$s$[/tex], the length of a side of the cube?
The formula for the volume of a cube is [tex]$V = s ^3$[/tex].
[tex]
\begin{array}{l}
s=\sqrt[3]{64} \\
s=64+64+64 \\
s=\sqrt{64} \\
s=64 \cdot 64 \cdot 64
\end{array}
[/tex]
Answer (2)
The volume of the cube is given as V = 64 cubic inches.
The formula for the volume of a cube is V = s 3 , where s is the side length.
To find the side length s , take the cube root of the volume: s = 3 V = 3 64 .
The expression representing the side length of the cube is s = 3 64 .
Explanation
Problem Analysis The problem states that the volume of a cube is 64 cubic inches and asks for the expression that represents the side length, s , of the cube. We know that the volume of a cube is given by the formula V = s 3 .
Setting up the equation We are given that V = 64 cubic inches. We need to find the expression for s such that s 3 = 64 . To find s , we take the cube root of both sides of the equation:
Solving for s Taking the cube root of both sides, we get:
s = 3 64
Final Answer Therefore, the expression that represents the length of a side of the cube is s = 3 64 .
Examples
Imagine you're designing a cubic storage container and you know it needs to hold 64 cubic inches of volume. To figure out the exact length of each side, you would use the cube root. This ensures your container is perfectly sized for its intended contents, demonstrating a practical application of cube root calculations in everyday design and engineering.
The expression that represents the length of a side of the cube is s = 3 64 . When calculated, this gives a side length of 4 inches. Thus, the correct option is the first one: s = 3 64 .
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