Math Problem Statement
The volume of this cube is 125 cubic feet. What is the value of z?
Solution
The question asks to determine the side length of a cube given its volume, which is .
The formula for the volume of a cube is:
Given , solve for :
Taking the cube root of both sides:
Thus, the value of is 5 feet.
Would you like further explanation or related examples? Here are five questions related to this concept:
- What is the formula for the surface area of a cube with a side length of ?
- If the volume of a cube is , what is the side length?
- How does the formula for the volume of a rectangular prism differ from that of a cube?
- What would happen to the volume if the side length of the cube doubles?
- Can a cube with a volume of have a side length that is not an integer?
Tip: Always check that the volume corresponds to the cube of an integer to quickly estimate the side length without a calculator.
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Math Problem Analysis
Mathematical Concepts
Geometry
Volume of a Cube
Exponents
Formulas
V = z^3
Theorems
Cube Root Theorem
Suitable Grade Level
Grade 7