Math Problem Statement

What is the volume of this object?

Solution

The object in the image appears to be a cube made of smaller unit cubes. To find the volume of the cube, we need to determine how many small cubes make up the large cube.

From the image, we can count the number of cubes along one edge of the large cube. It looks like there are 5 cubes along each edge.

The formula for the volume of a cube is:

V=s3V = s^3

where ss is the length of one side of the cube. In this case, s=5s = 5, so:

V=53=125cubic unitsV = 5^3 = 125 \, \text{cubic units}

Thus, the volume of the object is 125 cubic units.

Would you like any further details or explanations?

Here are 5 related questions you might explore:

  1. How does the volume change if the edge length is doubled?
  2. What is the surface area of this cube?
  3. If each small cube has a side length of 1 cm, what is the volume in cubic centimeters?
  4. How would the volume change if this object were a rectangular prism instead of a cube?
  5. How can the volume of a sphere be compared to that of a cube?

Tip: The volume of any 3D shape scales with the cube of its linear dimensions.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume Calculation

Formulas

Volume of a cube: V = s^3

Theorems

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Suitable Grade Level

Middle School