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Volume of a Rectangular Pyramid

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A 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. A rectangular pyramid is further classified into two types, i.e., a right rectangular pyramid and an oblique rectangular pyramid. A right rectangular pyramid is a rectangular pyramid that has its apex directly above the center of its base, whereas an oblique rectangular pyramid is a rectangular pyramid where the apex is not aligned right above the center 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

Volume of a Rectangular 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. The general 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 a Pyramid = 1/3 × Ah cubic units

where,
A” is the area of the base, and 
h” is the height of the pyramid.

Volume of a Rectangular Pyramid Formula

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

Area of a rectangle = l × w

where,
l” is the length of the rectangle’
w” is its width.

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

where,
l” is the base length,
w” is the base width,
h” is the height of the pyramid.

How to Find the Volume of a Rectangular 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 the above steps Volume of the Rectangular Pyramid is found.

Solved Examples of Volume of Rectangular Pyramid

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

Solution:

Given data,

Area of the rectangular base = 60 cm2

The height of the pyramid = 10 cm

We know that,

V = (1/3) × Ah

   = (1/3) × 60 × 10

   = 20 × 10 = 200 cm3

Hence, the volume of the 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 data,

Base length (l) = 12 cm

Base width (w) = 8 cm

The height of the pyramid (h) = 15 cm

We know that,

The volume of the rectangular pyramid (V)= (1/3) × lwh cubic units

= (1/3) × 12 × 8 × 15

= (1/3) × 1440 

= 480 cm3

Hence, the volume of the 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 data,

Base length (l) = 9 inches

Base width (w) = 5 inches

The height of the pyramid (h) = 12 inches

We know that,

The volume of the rectangular pyramid (V)= (1/3)lwh cubic units

= (1/3) × 9 × 5 × 12

= (1/3) × 540

= 180 in3

Hence, the volume of the 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 data,

Area of the rectangular base = 150 cm2

The volume of the 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, the height of the 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 data,

Base length (l) = 15 m

Base width (w) = 10 m

The height of the pyramid (h) = 20 m

We know that,

The volume of the rectangular pyramid (V)= (1/3)lwh cubic units

= (1/3) × 15 × 10 × 20

= (1/3) × 3000

= 1,000 m3

Hence, the 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:

The 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

Where “A” is the area of the base, and “h” is the height of the pyramid. 

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

FAQs on Volume of Rectangular Pyramid

Question 1: What is the definition of a rectangular pyramid?

Answer:

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.

Question 2: Define the Volume of a Rectangular Pyramid.

Answer:

The 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:

The volume of the rectangular pyramid (V)= (1/3)lwh cubic units

Where “l” is the base length,

“w” is the base width, and

“h” is the height of the pyramid.

Question 3: What are the types of rectangular pyramids?

Answer:

There are two types of rectangular pyramids, namely, a right rectangular pyramid and an oblique rectangular pyramid.

Question 4: Define a Right Rectangular Pyramid.

Answer:

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

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Last Updated : 06 Jan, 2024
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