Math Problem Statement

Find the volume of the shape.

"8"

"8"

"8"

Question content area bottom

Part 1

The volume of the shape is

enter your response here

in. cubed

Solution

To find the volume of the shape, we need to determine whether the dimensions 8×8×88 \times 8 \times 8 represent a cube. Assuming it is a cube, the volume is calculated using the formula:

Volume=side3\text{Volume} = \text{side}^3

Calculation:

Volume=83=8×8×8=512in3\text{Volume} = 8^3 = 8 \times 8 \times 8 = 512 \, \text{in}^3

Final Answer:

The volume of the shape is: 512in3\boxed{512 \, \text{in}^3}

Would you like a detailed explanation of how the formula works or any further clarifications?

Here are 5 related questions to deepen understanding:

  1. What is the formula for the volume of a rectangular prism?
  2. How do we calculate the surface area of a cube with side length 8?
  3. What happens to the volume if one dimension of the cube doubles?
  4. Can the same formula apply to shapes that aren't cubes? Why or why not?
  5. How would the volume change if the side length is reduced to 4?

Tip: Always ensure all dimensions have the same units before performing volume calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of 3D Shapes
Cubes

Formulas

Volume of a cube = side^3

Theorems

Exponential properties of multiplication

Suitable Grade Level

Grades 5-7