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,
- Area of Rectangular Base = 60 cm2
- Height of Pyramid = 10 cm
We know that,
V = (1/3) Ć Ah
V = (1/3) Ć 60 Ć 10
V = 20 Ć 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) Ć l.w.h cubic units
V = (1/3) Ć 12 Ć 8 Ć 15
V = (1/3) Ć 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)Ćl.w.h cubic units
V = (1/3) Ć 9 Ć 5 Ć 12
V = (1/3) Ć 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) Ć Ah
450 = (1/3) Ć 150 Ć h
450 = 50 Ć 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) Ć 15 Ć 10 Ć 20
V = (1/3) Ć 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 ā h
ā V1/V2 = h1/h2
ā V/V2 = h/2h
ā V/V2 = 1/2
ā V2 = 2V
So, volume of a rectangular pyramid will be doubled if its height gets doubled and the base area remains constant.
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.
Table of Content
- Rectangular Pyramid Definition
- Volume of a Rectangular Pyramid
- Volume of a Rectangular Pyramid Formula
- How to Find the Volume of a Rectangular Pyramid?
- Examples of Volume of Rectangular Pyramid