Math Problem Statement

The volume of this cube is 512 cubic centimeters. What is the value of t?

Solution

To find the value of tt, we can use the formula for the volume of a cube, which is:

V=t3V = t^3

Given that the volume of the cube is 512 cubic centimeters, we can set up the equation:

t3=512t^3 = 512

Now, solve for tt by taking the cube root of both sides:

t=5123t = \sqrt[3]{512}

Since 512=83512 = 8^3, we have:

t=8 centimeterst = 8 \text{ centimeters}

Therefore, the value of tt is 88 centimeters.

Would you like further details or have any questions?

Here are 5 related questions to consider:

  1. What is the formula for the surface area of a cube with side length tt?
  2. If the side length tt was doubled, what would the new volume be?
  3. How would the volume change if tt was halved?
  4. What is the cube root of 729? How does it relate to finding the side length of a cube with volume 729?
  5. Can you express the volume formula for a rectangular prism instead of a cube?

Tip: To solve cube volume problems, always remember to take the cube root to find the side length.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of a Cube
Algebra

Formulas

V = t^3
t = \sqrt[3]{V}

Theorems

Cube Root Theorem

Suitable Grade Level

Grades 6-8