Table of Contents

Last modified on August 3rd, 2023

The volume of a pentagonal prism is the space it occupies in the three-dimensional plane. It is measured in cubic units such as m^{3}, cm^{3}, mm^{3}, ft^{3}.

The formula is given below:

Let us solve some examples to understand the concept better.

**Find the volume of a regular pentagonal prism given in the figure.**

Solution:

As we know,

Volume (*V*) = ${\dfrac{5}{2}abh}$*,*, here, a = 6.193 m, b = 9 m, h = 20 m

${\therefore V= \dfrac{5}{2}\times 6.193\times 9\times 20}$

= 2786.85 m^{3}

Finding the volume of a pentagonal prism when the** BASE EDGE** and **HEIGHT** are known

**Find the volume of a regular pentagonal prism with a base edge of 4 cm and a height of 7 cm.**

Solution:

Here we will use an alternative formula.

Volume (*V*) = ${\dfrac{1}{4}\sqrt{5\left( 5+2\sqrt{5}\right) }b^{2}h}$ , here *b* = 4 cm, *h* = 7 cm

${\therefore V= \dfrac{1}{4}\sqrt{5\left( 5+2\sqrt{5}\right) }\times 4^{2}\times 7 }$

≈ 192.7 cm^{3}

Finding the volume of an oblique pentagonal prism when the** BASE EDGE** and **HEIGHT** are known

**Find the volume of the oblique pentagonal prism given in the figure.**

Solution:

As we know,

The volume of an oblique pentagonal prism = the volume of a right pentagonal prism having the height ‘h’

Using the alternative formula

Volume (*V*) = ${ \dfrac{1}{4}\sqrt{5\left( 5+2\sqrt{5}\right) }b^{2}h }$ , here b = 6 m, h = 13 m

${\therefore V= \dfrac{1}{4}\sqrt{5\left( 5+2\sqrt{5}\right) }\times 6^{2}\times 13 }$

= 805.2 m^{3}

**More Resources:**- Volume of a Prism
- Surface Area of a Prism
- Right Prism
- Oblique Prism
- Rectangular Prism
- Volume of a Rectangular Prism
- Surface Area of a Rectangular Prism
- Triangular Prism
- Volume of a Triangular Prism
- Surface Area of a Triangular Prism
- Hexagonal Prism
- Volume of a Hexagonal Prism
- Surface Area of a Hexagonal Prism
- Pentagonal Prism
- Volume of a Pentagonal Prism
- Surface Area of a Pentagonal Prism
- Trapezoidal Prism
- Volume of a Trapezoidal Prism
- Surface Area of a Trapezoidal Prism
- Square Prism
- Volume of a Square Prism
- Surface Area of a Square Prism
- Octagonal Prism
- Heptagonal Prism
- Decagonal Prism

Last modified on August 3rd, 2023