Volume of Rectangular Prism

The volume of a rectangular prism is the measurement of the total space inside it. Imagine a rectangular container filled with water. In this case, the total quantity of water that the container can hold is its volume. A prism is a polyhedron having identical bases, flat rectangular side faces, and the same cross-section all along its length. Prisms are classified on the basis of the shape of their base. A rectangular prism is categorized as a three-dimensional shape. It has six faces and all the faces of the prism are rectangles. Let us learn the formula to find the volume of a rectangular prism in this article.

The volume of a rectangular prism is defined as the space occupied within a rectangular prism. A rectangular prism is a polyhedron that has two pairs of congruent and parallel bases. It has 6 faces (all are rectangular),12 sides, and 8 vertices. As the rectangular prism is a three-dimensional shape (3D shape), the unit that is used to express the volume of the rectangular prism is cm³, m³ and so on. In mathematics, any polyhedron, having all such characteristics can be referred to as a Cuboid.

The formula for the volume of a rectangular prism = base area × height of the prism. Since the base of a rectangular prism is a rectangle, its area will be l × w. This area is then multiplied by the height of the prism to get the volume of the prism. Therefore, another way to express this formula is by multiplying the length, width, and height of the prism and write the value in cubic units (cm³, m³, in³, etc).

Therefore, the formula for the volume of a rectangular prism is, volume of a rectangular prism (V) = l × w × h, where

• “l” is the base length
• “w” is the base width
• “h” is the height of the prism

To find the volume of the rectangular prism, we multiply the length, width, and height, that is the area of the base is multiplied by the height. It should be noted that the volume is measured in cubic units.

There are two types of rectangular prisms - right rectangular prisms and oblique prisms.

• In the case of a right rectangular prism, the bases are perpendicular to the other faces.
• In the case of an oblique rectangular prism, the bases are not perpendicular to the other faces. Thus, the perpendicular drawn from the vertex of one base to the other base of the prism will be taken as its height.

It should be noted that we can apply the same formula to calculate the volume of the prism, that is the rectangular prism volume formula, v = lwh, irrespective of the type of rectangular prism.

Before calculating the volume of a rectangular prism using the formula, we need to make sure that all the dimensions are of the same units. The following steps are used to calculate the volume of a rectangular prism.

• Step 1: Identify the type of the base and find its area using a suitable formula (as explained in the previous section).
• Step 2: Identify the height of the prism, which is perpendicular from the top vertex to the base of the prism.
• Step 3: Multiply the base area and the height of the prism to get the volume of the rectangular prism in cubic units. Volume = base area × height of the prism

Example: Calculate the volume of a rectangular prism whose height is 8 in and whose base area is 90 square inches.

Solution: We can calculate the volume of the rectangular prism using the following steps:

• Step 1: The base area is already given as 90 square inches.
• Step 2: The height of the prism is 8 in.
• Step 3: The volume of the given rectangular prism = base area × height of the prism = 90 × 8 = 720 cubic inches.

What is the Volume of a Rectangular Prism?

The volume of a rectangular prism is the capacity that it can hold or the space occupied by it. Thus, the volume of a rectangular prism can be calculated by multiplying its base area by its height. The formula that is used to find the volume of a rectangular prism is, Volume (V) = height of the prism × base area. It is expressed in cubic units such as cm³, m³, in³, etc.

What is the Formula for the Volume of a Rectangular Prism?

The formula for the volume of a rectangular prism is, Volume (V) = base area × height of the prism. Another way to express this formula is, Volume = l × w × h; where 'l' is the length, 'w' is the width, and 'h' is the height of the prism.

How to Find the Volume of a Rectangular Prism?

In order to find the volume of a rectangular prism, follow the steps given below:

• Step 1: Identify the length (l) and width (w) of the base of the prism.
• Step 2: Find the height (h) of the prism.
• Step 3: Substitute the respective values in the formula, V = lwh
• Step 4: Find the product of these values to get the volume of the prism in cubic units.

How to Find the Height of a Rectangular Prism when the Volume of a Rectangular Prism is given?

The height of a rectangular prism can be calculated if the volume of the prism is given using the same formula, Volume (V) = base area × height of the prism. For example, the volume of a prism is 600 cubic units and its base area is 60 square units. Then, after substituting the values in the equation, we get 600 = 60 × height of the prism. This means, height = 600/60 = 10. Therefore, the height is 10 units.

What Happens to the Volume of Rectangular Prism if its Height is Doubled?

We know that the volume of a rectangular prism is the product of its three dimensions, that is, volume = length × width × height. If its height is doubled, its volume will be l × w × (2h) = 2lwh = 2 × v. Thus, we can say that the volume of the rectangular prism also gets doubled when its height is doubled.

What Happens to the Volume of Rectangular Prism if the Length is Doubled and the Height is Reduced to One Half?

The formula for calculating the volume of a rectangular prism is volume = length × width × height. If its length is doubled, and the height is reduced to half, then its volume can be written as, V = (2l) × (w) × (1/2h). After simplifying this, we get l × w × h which is the regular formula for volume. Thus, we can say that the volume of the rectangular prism will remain the same if its length gets doubled and the height is reduced to half.

What Happens to the Volume of Rectangular Prism if the Length, Width, and Height of Prism are Doubled?

The volume of a rectangular prism is the product of its three dimensions, that is volume = length × width × height. If its length, width, and height is doubled, then its volume will be (2l) × (2w) × (2h) = 8lwh = 8 × v. Thus, we can conclude that if its length, width, and height is doubled, the volume of the rectangular prism will be 8 times the original value.

How to Find the Volume of a Rectangular Prism with Fractions?

The volume of a rectangular prism can be calculated even if the values are given in fractions. For example, if the length of a rectangular prism is \(1\dfrac{3}{5}\) units, the width is 3/4, and its height is 2/3 units, the volume of the prism = l × w × h = \(1\dfrac{3}{5}\) × 3/4 × 2/3. Now, let us convert the mixed fraction into an improper fraction and then multiply all the fractions. We will first multiply the numerators and then the denominators and then reduce the resultant fraction, if needed. This means Volume = 8/5 × 3/4 × 2/3 = 48/60 = 4/5. Therefore the volume of the prism is 4/5 cubic units.