Volume of a Cuboid Calculator

Published on: August 18, 2024
Final Answer: Free • Full Steps: Plus

This Volume of a Cuboid Calculator finds the space inside a cuboid from its length, width and height, and shows the working line by line. A cuboid is a stack of identical layers, so the area of the base is worked out first and then multiplied by the height to count every layer. The answer is written in cubic units. Following the same pattern every time is what makes the volume of a cuboid easy to picture, check, and work out on your own.

Cuboid labeled l, w, h

In the diagram, the dimensions are labeled \(l\), \(w\) and \(h\).

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the length, the width and the height into the formula.
  4. Multiply the length by the width to get the area of the base.
  5. Multiply by the height to get the volume.

Formula:

\(V = l \times w \times h\)
See Example 1 Hide Example 1

Problem

\(l = 8, w = 5, h = 3\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the length, the width and the height into the formula.
  4. Multiply the length by the width to get the area of the base.
  5. Multiply by the height to get the volume.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the volume of a cuboid whose length is \(l = 8\), whose width is \(w = 5\) and whose height is \(h = 3\).

\(l = 8,\; w = 5,\; h = 3\)

Step 2

Step 2 - Write the formula.

In this problem: A cuboid is a stack of identical layers, so its volume is the area of the base multiplied by the height, which is the length times the width times the height.

\(V = l \times w \times h\)

Step 3

Step 3 - Substitute the length, the width and the height into the formula.

In this problem: Replacing \(l\), \(w\) and \(h\) with \(8\), \(5\) and \(3\) in \(V = l \times w \times h\) gives \(V = 8 \times 5 \times 3\).

\(V = 8 \times 5 \times 3\)

Step 4

Step 4 - Multiply the length by the width to get the area of the base.

In this problem: Multiplying the length by the width gives the area of the base: \(8 \times 5 = 40\).

\(V = 40 \times 3\)

Step 5

Step 5 - Multiply by the height to get the volume.

In this problem: Multiplying that base area by the height gives \(40 \times 3 = 120\).

\(V = 40 \times 3 = 120\)

Final Answer

\(V = 120\)
See Example 2 Hide Example 2

Problem

\(l = 2, w = 2.5, h = 4\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the formula.
  3. Substitute the length, the width and the height into the formula.
  4. Multiply the length by the width to get the area of the base.
  5. Multiply by the height to get the volume.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the volume of a cuboid whose length is \(l = 2\), whose width is \(w = 2.5\) and whose height is \(h = 4\).

\(l = 2,\; w = 2.5,\; h = 4\)

Step 2

Step 2 - Write the formula.

In this problem: A cuboid is a stack of identical layers, so its volume is the area of the base multiplied by the height, which is the length times the width times the height.

\(V = l \times w \times h\)

Step 3

Step 3 - Substitute the length, the width and the height into the formula.

In this problem: Replacing \(l\), \(w\) and \(h\) with \(2\), \(2.5\) and \(4\) in \(V = l \times w \times h\) gives \(V = 2 \times 2.5 \times 4\).

\(V = 2 \times 2.5 \times 4\)

Step 4

Step 4 - Multiply the length by the width to get the area of the base.

In this problem: Multiplying the length by the width gives the area of the base: \(2 \times 2.5 = 5\).

\(V = 5 \times 4\)

Step 5

Step 5 - Multiply by the height to get the volume.

In this problem: Multiplying that base area by the height gives \(5 \times 4 = 20\).

\(V = 5 \times 4 = 20\)

Final Answer

\(V = 20\)

Example Problems

Click one to load it into the box and solve it.