Rectangular Prism

Calculate the volume and surface area of a rectangular prism easily with the calculator on Examples.com. Get accurate results instantly by entering the dimensions of your rectangular prism for quick calculations.

A rectangular prism, also known as a cuboid, is a three-dimensional solid shape with six rectangular faces, twelve edges, and eight vertices. It has three dimensions: length, width, and height, which are perpendicular to each other. Rectangular prisms are commonly found in everyday objects such as boxes, books, and buildings. The shape has congruent and parallel opposite faces, and all interior angles are 90 degrees. In mathematics, rectangular prisms are often used to calculate volume and surface area, making them important in geometry, construction, and packaging industries due to their ability to efficiently occupy space.

How to Use the Rectangular Prism

Step 1: Input the Length

Begin by entering the length of the rectangular prism in the “Length (l)” field.

Step 2: Input the Width

Next, input the width in the “Width (w)” field.

Step 3: Input the Height

Now, provide the height of the rectangular prism in the “Height (h)” field.

Formula:

The tool will calculate the Surface Area using the formula:
Surface Area = 2(lw+lh+wh)
and the Volume using the formula:
Volume = l×w×h

Step 4: View Results

After you’ve entered the dimensions, the surface area and volume will be displayed automatically below the input fields.

Rectangular Prism Formula

Surface Area of a Rectangular Prism:

The surface area of a rectangular prism is calculated by summing the areas of all six rectangular faces using the formula:

Surface Area=2(Length×Width+Length×Height+Width×Height)

Volume of a Rectangular Prism:

The volume of a rectangular prism is found by multiplying its length, width, and height. The formula is:

Volume=Length×Width×Height

Properties of a Rectangular Prism

1. Faces: A rectangular prism has 6 faces, all of which are rectangles.
2. Edges: It has 12 edges, with opposite edges being equal in length.
3. Vertices: A rectangular prism has 8 vertices (corners).
4. Right Angles: All angles in a rectangular prism are 90 degrees.
5. Faces Arrangement: Opposite faces are congruent (equal in size and shape).
6. Shape: It is a three-dimensional solid object with rectangular bases.
7. Volume: Calculated as l×w×h where l = length, w = width, and h = height.
8. Surface Area: Calculated as 2(lw+lh+wh).
9. Symmetry: A rectangular prism is symmetrical along its center axes.
10. Parallel Faces: Opposite faces are parallel to each other.

Types of a Rectangular Prism

1. Right Rectangular Prism

• All angles are 90 degrees, and the faces are rectangular.
• The edges are perpendicular to the base.

2. Oblique Rectangular Prism

• The faces are still rectangles, but the sides are slanted, meaning the edges are not perpendicular to the base.

3. Cube (Special Case of a Rectangular Prism)

• All six faces are squares, meaning the length, width, and height are equal.
• A cube is a perfect type of rectangular prism with equal dimensions.

Examples of Rectangular Prism

Example 1: Finding the Volume of a Rectangular Prism

Problem:
A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 10 cm. What is its volume?

Solution:
The formula to find the volume of a rectangular prism is: Volume = Length × Width × Height

Substituting the given values: Volume = 8 cm × 5 cm × 10 cm = 400 cm³

Answer: The volume of the rectangular prism is 400 cm³.

Example 2: Finding the Surface Area of a Rectangular Prism

Problem:
Find the surface area of a rectangular prism with a length of 7 m, a width of 4 m, and a height of 3 m.

Solution:
The formula to find the surface area is: Surface Area = 2(Length × Width + Length × Height + Width × Height)

Substitute the given values: Surface Area = 2(7 × 4 + 7 × 3 + 4 × 3)
= 2(28 + 21 + 12) = 2(61) = 122 m²

Answer: The surface area of the rectangular prism is 122 m².

Example 3: Finding a Missing Dimension Given the Volume

Problem:
A rectangular prism has a volume of 600 cubic inches. Its length is 10 inches, and its width is 5 inches. What is the height of the rectangular prism?

Solution:
Use the volume formula:
Volume = Length × Width × Height

Rearrange the formula to solve for height:
Height = Volume / (Length × Width)

Substitute the known values:
Height = 600 / (10 × 5) = 600 / 50 = 12 inches

Answer: The height of the rectangular prism is 12 inches.

Example 4: Calculating the Diagonal of a Rectangular Prism

Problem:
What is the length of the diagonal of a rectangular prism with dimensions 6 cm, 8 cm, and 10 cm?

Solution:
The diagonal (d) of a rectangular prism can be found using the Pythagorean theorem in three dimensions: d = √(L² + W² + H²)

Substitute the given values:
d = √(6² + 8² + 10²) = √(36 + 64 + 100) = √200 = 14.14 cm

Answer: The diagonal of the rectangular prism is approximately 14.14 cm.

Example 5: Finding the Length Given the Surface Area

Problem:
A rectangular prism has a surface area of 94 square feet, a width of 3 feet, and a height of 4 feet. Find the length.

Solution:
The surface area formula is:
Surface Area = 2(Length × Width + Length × Height + Width × Height)

Substitute the known values and solve for length:
94 = 2(L × 3 + L × 4 + 3 × 4)
94 = 2(3L + 4L + 12) = 2(7L + 12)
94 = 14L + 24
70 = 14L
L = 70 / 14 = 5 feet

Answer: The length of the rectangular prism is 5 feet.

What is the rule for rectangular prism?

The rule for a rectangular prism is that it has six rectangular faces, twelve edges, and eight vertices. Its opposite faces are congruent and parallel.

How many edges does a rectangular prism have?

A rectangular prism has 12 edges, where three sets of parallel edges correspond to its length, width, and height.

Is a rectangular prism also a cuboid?

Yes, a rectangular prism is also called a cuboid. Both terms describe a 3D shape with six rectangular faces and right angles at each vertex.

How many bases does a rectangular prism have?

A rectangular prism has two bases. These bases are opposite, congruent, and parallel rectangular faces of the prism.

How can a rectangular prism be used in math problems?

Rectangular prisms are commonly used in geometry and volume-related math problems to help calculate surface area, volume, and diagonal distances. These problems are typically applied in real-world scenarios such as packaging and construction.

Can a rectangular prism have equal dimensions?

Yes, when all three dimensions (length, width, and height) of a rectangular prism are equal, the rectangular prism becomes a cube. In this case, all faces are squares, and it has equal sides.

What is a rectangular prism also known as?

A rectangular prism is also known as a cuboid. In some contexts, it’s referred to simply as a box or rectangular box.

How does changing one dimension affect the volume of a rectangular prism?

If one dimension of a rectangular prism is changed while keeping the other two dimensions constant, the volume changes proportionally to the change in that dimension. For example, doubling the height while keeping the length and width the same will double the volume.

What is the ratio of corners to faces in rectangular prisms?

The ratio of corners (vertices) to faces in a rectangular prism is 8:6, meaning it has 8 vertices and 6 faces.

What is the net of a rectangular prism?

A net of a rectangular prism is a two-dimensional representation of the prism that shows all six faces laid out flat. It consists of three pairs of rectangles, each corresponding to the faces of the prism.