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 zz of a cube given its volume, which is 125cubic feet125 \, \text{cubic feet}.

The formula for the volume of a cube is:

V=z3V = z^3

Given V=125V = 125, solve for zz:

z3=125z^3 = 125

Taking the cube root of both sides:

z=1253=5z = \sqrt[3]{125} = 5

Thus, the value of zz is 5 feet.

Would you like further explanation or related examples? Here are five questions related to this concept:

  1. What is the formula for the surface area of a cube with a side length of zz?
  2. If the volume of a cube is 64cubic units64 \, \text{cubic units}, what is the side length?
  3. How does the formula for the volume of a rectangular prism differ from that of a cube?
  4. What would happen to the volume if the side length of the cube doubles?
  5. Can a cube with a volume of 27cubic meters27 \, \text{cubic meters} 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