Solved Examples on Pentagonal Pyramid
Example 1: What is the volume of a pentagonal pyramid if the base area is 125 cm2 and the height of the pyramid is 10 cm?
Solution:
Given data,
Area of the pentagonal base = 125 cm2
Height of the pyramid = 10 cm
We know that,
The volume of a pentagonal pyramid (V) = 1/3 × Area of pentagonal base × Height
V = 1/3 × 125 × 10 = 416.67 cm3
Hence, the volume of the given pentagonal pyramid is 416.67 cm3.
Example 2: What is the volume of a pentagonal pyramid whose apothem length is 5 in, base length is 10 in, and height is 12 in?
Solution:
Given data,
Apothem length (a) = 5 in
Base length (s) = 10 in,
Height (h) = 12 in,
We know that,
The volume of a pentagonal pyramid (V) = (5/6) ash cubic units
= (5/6) × 5 × 10 × 12
= 500 cu. in
Therefore, the volume of this pentagonal pyramid is 500 cu. in.
Example 3: Find the volume of a pentagonal pyramid if its base area is 135 cm2 and the height of the pyramid is 13 cm.
Solution:
Given data,
Area of the pentagonal base = 135 cm2
Height of the pyramid = 13 cm
The volume of a pentagonal pyramid (V) = 1/3 × Area of pentagonal base × Height
V = 1/3 × 135 × 13 = 585 cm3
Hence, the volume of the given pentagonal pyramid is 585 cm3.
Example 4: Find the height of a pentagonal pyramid if its base area is 150 m2 and the volume is 600 m3.
Solution:
Given data,
Area of the pentagonal base = 150 m2
The volume of a pentagonal pyramid (V) = 600 m3
We know that,
The volume of a pentagonal pyramid (V) = 1/3 × Area of pentagonal base × Height
⇒ 600 = (1/3) × 150 × h
⇒ 50h = 600
⇒ h = 600/50 = 12 m
Hence, the height of the given pentagonal pyramid is 12 m.
Example 5: Calculate the volume of a pentagonal pyramid whose apothem length is 7 cm, base length is 8 cm, and height is 15 cm.
Solution:
Given data,
Apothem length (a) = 7 cm
Base length (s) = 8 cm,
Height (h) = 15 cm,
We know that,
The volume of a pentagonal pyramid (V) = (5/6) ash cubic units
= (5/6) × 7 × 8 × 15
= 700 cu. cm
Therefore, the volume of this pentagonal pyramid is 700 cu. cm.
Volume of a Pentagonal Pyramid
A pentagonal pyramid is a three-dimensional geometric figure that has a pentagonal base with five triangular faces that meet at a point. The meeting point is known as the apex, which joins the triangular faces and the pentagonal base. It has six faces (five triangular faces and a pentagonal base), six vertices, and ten edges.
Table of Content
- Pentagonal pyramid’s real-life applications:
- Volume of a Pentagonal Pyramid
- Types of Pentagonal Pyramid
- A regular pentagonal pyramid
- An irregular pentagonal pyramid
- A right pentagonal pyramid
- How to Find the Volume of the Pentagonal Pyramid?
- Solved Examples on Pentagonal Pyramid