Volume of a Rectangular Pyramid

Rectangular pyramid is a three-dimensional object that has a rectangular base upon which are erected four triangular faces that meet at a common point called the apex. It has a total of five faces, i.e., a rectangular base, four triangular faces, five vertices, and eight edges. In a rectangular pyramid, all the triangular faces are congruent to the opposite face.

Volume of the rectangular pyramid is the space occupied by the rectangular pyramid and its formula is covered in this article.

Rectangular pyramid is a 3-D shape with a rectangle base and triangular faces that meet at a common point called the apex. Rectangular pyramid is classified into two types:

• Right Rectangular Pyramid
• Oblique Rectangular Pyramid

A right rectangular pyramid is a rectangular pyramid that has its apex directly above the centre of its base. In contrast, an oblique rectangular pyramid is a rectangular pyramid where the apex is not aligned right above the centre of its base. The height of an oblique rectangular pyramid is the perpendicular line drawn from the apex to the base of the pyramid.

Volume of a rectangular pyramid is defined as the total space enclosed between all the faces of a pyramid. The volume of a pyramid is generally represented by the letter “V” and is measured in terms of cubic units like cm³, m³, ft³, in³, etc.

Formula to calculate the volume of a pyramid is equal to one-third the product of the area of the base and the height of the pyramid.

Volume of Pyramid = 1/3 × Ah cubic units

where,

• A is Area of Base
• h is Height of Pyramid

Formula for finding the volume of a rectangular pyramid is discussed below in the article. As we know,

Area of Rectangle = l × w

And the volume of the rectangular pyramid is 1/3 of the product of the base and height of the rectangular pyramid. So, the volume of the rectangular pyramid (V)= 1/3 (l × w) h cubic units

Volume of Rectangular Pyramid (V) = (1/3) × lwh cubic units

where,

• l is Length of Rectangle Base
• w is Width of Rectangle Base
• h is Height of Pyramid

The volume of a rectangular pyramid is found using the formula Volume = 1/3 × base area × height. Follow the steps below to find the volume of a rectangular pyramid.

Step 1: Determine the area of the rectangular base using the formula Area of rectangle = (L × B)

Step 2: Find the volume using the formula, Volume = 1/3 × (Base Area) × (h)

Step 3: Final answer is obtained and is represented in cubic units.

Using above steps Volume of the Rectangular Pyramid is found.

Related Read:

• Surface Area of Pyramid
• Volume of Pyramid
• Square Pyramid

Example 1: Determine the volume of a rectangular pyramid whose base area and height are 60 cm² and 10 cm, respectively.

Solution:

Given,

• Area of Rectangular Base = 60 cm²
• Height of Pyramid = 10 cm

We know that,

V = (1/3) × Ah

V = (1/3) × 60 × 10

V = 20 × 10 = 200 cm³

Hence, volume of given rectangular pyramid is 200 cm³.

Example 2: Find the volume of a rectangular pyramid if the base length is 12 cm and the base width is 8 cm, and the height of the pyramid is 15 cm.

Solution:

Given,

• Base length (l) = 12 cm
• Base width (w) = 8 cm
• Height of Pyramid (h) = 15 cm

We know that,

Volume of Rectangular Pyramid (V) = (1/3) × l.w.h cubic units

V = (1/3) × 12 × 8 × 15

V = (1/3) × 1440 

V = 480 cm³

Hence, volume of given rectangular pyramid is 480 cm³.

Example 3: Find the volume of a rectangular pyramid if the base length is 9 inches and the base width is 5 inches, and the height of the pyramid is 12 inches.

Solution:

Given,

• Base length (l) = 9 inches
• Base width (w) = 5 inches

Height of Pyramid (h) = 12 inches

We know that,

Volume of Rectangular Pyramid (V) = (1/3)×l.w.h cubic units

V = (1/3) × 9 × 5 × 12

V = (1/3) × 540

V = 180 in³

Hence, volume of given rectangular pyramid is 180 in³.

Example 4: Determine the height of a rectangular pyramid whose base area and volume are 150 cm² and 450 cm3, respectively.

Solution:

Given,

• Area of Rectangular Base = 150 cm²
• Volume of Rectangular Pyramid = 450 cm³

We know that,

V = (1/3) × Ah

450 = (1/3) × 150 × h

450 = 50 × h

h = 450/50 = 9 cm

Hence, height of given rectangular pyramid is 9 cm.

Example 5: What is the volume of a rectangular pyramid if the base length is 15 m and the base width is 10 m, and the height of the pyramid is 20 m?

Solution:

Given,

• Base length (l) = 15 m
• Base width (w) = 10 m
• Height of the pyramid (h) = 20 m

We know that,

Volume of Rectangular Pyramid (V) = (1/3)lwh cubic units

V = (1/3) × 15 × 10 × 20

V = (1/3) × 3000

V = 1,000 m³

Hence, volume of the given rectangular pyramid is 1,000 m³

Example 5: What happens to the volume of a rectangular pyramid if its height gets doubled and the base area remains constant?

Solution:

Volume of a rectangular pyramid will be doubled if its height gets doubled and the base area remains constant.

We know that,

V = (1/3) Ah

So, volume of the pyramid is directly proportional to its height, i.e., V ∝ h

⇒ V₁/V₂ = h₁/h₂

⇒ V/V₂ = h/2h

⇒ V/V₂ = 1/2

⇒ V₂ = 2V

So, volume of a rectangular pyramid will be doubled if its height gets doubled and the base area remains constant.

What is a Rectangular Pyramid?

A rectangular pyramid is a three-dimensional geometric figure that has a rectangular base and four triangular faces that meet at a common vertex called the apex.

How to Find the Volume of a Rectangular Pyramid?

Volume of a rectangular pyramid is defined as the total space enclosed between all the faces of a pyramid. It can be calculated using the formula given below:

Volume of Rectangular Pyramid (V) = (1/3)lwh cubic units

What are Types of Rectangular Pyramids?

There are two types of rectangular pyramids:

• Right Rectangular Pyramid
• Oblique Rectangular Pyramid

What is a Right Rectangular Pyramid?

A right rectangular pyramid is a rectangular pyramid that has its apex directly above the center of its base.