Math Problem Statement

solve it

The solid below is made from cubes. Find its volume.

Solution

The image shows a rectangular prism made of unit cubes, with the base dimensions of 1 meter and cubes arranged in a grid.

To find the volume of the rectangular prism, we need to calculate the number of unit cubes that make up the entire structure. Each cube represents 1 cubic meter (m³).

The rectangular prism has:

  • Length: 4 cubes (each cube is 1 meter, so total length is 4 meters),
  • Width: 2 cubes (total width is 2 meters),
  • Height: 2 cubes (total height is 2 meters).

The formula for the volume of a rectangular prism is:

V=length×width×heightV = \text{length} \times \text{width} \times \text{height}

Substituting the values:

V=4m×2m×2m=16m3V = 4 \, \text{m} \times 2 \, \text{m} \times 2 \, \text{m} = 16 \, \text{m}^3

Thus, the volume of the rectangular prism is 16m316 \, \text{m}^3.

Do you want more details or have any questions?

Here are 5 related questions to expand on this:

  1. How would the volume change if the height were doubled?
  2. What is the surface area of this rectangular prism?
  3. How does the volume change if each dimension is increased by 50%?
  4. What is the formula for the volume of a cube and how does it compare to the prism's volume formula?
  5. If the unit cubes had a different size, how would that affect the total volume?

Tip: The volume of any solid object can be found by multiplying its dimensions (length, width, height). Always make sure the units are consistent!

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume Calculation
Rectangular Prism

Formulas

Volume of a rectangular prism: V = length × width × height

Theorems

Basic volume calculation theorem for prisms

Suitable Grade Level

Grades 5-7