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Last modified on August 3rd, 2023

The volume of a pyramid is the space it occupies in a 3-dimensional plane. It is expressed in cubic units such as m^{3}, cm^{3}, mm^{3}, and in^{3}.

The general formula to find the volume of any pyramid is:

**Volume ( V) = ${\dfrac{1}{3}Bh}$,** here B = base area, h = height

However, there are specific formulas to calculate the volume of different pyramids due to their different shapes. They are:

Let us solve some examples to understand the above concept better.

**Find the volume of a triangular pyramid with a base area of 64 cm ^{2}**

Solution:

As we know,

Volume (*V*) = ${\dfrac{1}{3}Bh}$, here B = 64 cm^{2}, h = 6.3 cm

∴ *V* = ${\dfrac{1}{3}\times 64\times 6.3}$

= 134.4 cm^{3}

Finding the volume of a triangular pyramid when the **BASE LENGTH**,** BASE HEIGHT **and **HEIGHT** are known

**Find the volume of a triangular pyramid whose height is 6 cm, base length is 7 cm, and base height is 8.5 cm.**

Solution:

As we know,

Volume (*V*) =** ** ${\dfrac{1}{6}bHh}$** , **here b = 7 cm, H = 6 cm, h = 8.5 cm

∴ V = ${\dfrac{1}{6}\times 7\times 6\times 8.5}$

= 59.5 cm

Finding the volume of an equilateral triangular pyramid when the **BASE LENGTH** and **HEIGHT** are known

**Find the volume of a triangular pyramid whose height is 18 cm, and base is 4 cm each.**

Solution:

As we know,

The area of an equilateral triangle = ${\dfrac{\sqrt{3}}{4}b^{2}}$, here a = side of the triangle

Using this formula,

Volume (*V*) = ${\dfrac{\sqrt{3}}{12}b^{2}h}$** **,** **here b = 4 cm, h = 18 cm

∴ V = ${\dfrac{\sqrt{3}}{12}\times 4^{2}\times 18}$** **

= 18.47 cm^{3}

**Find the volume of a square pyramid whose height is 13 cm, and base is 5 cm.**

Solution:

As we know,

Volume (*V*) = ${\dfrac{1}{3}b^{2}h}$, here b = 5 cm, h = 13 cm

∴ V = ${\dfrac{1}{3}\times 5^{2}\times 13}$

= 108.33 cm^{3}

**Find the volume of a rectangular pyramid whose height is 8 cm, and bases are 6 cm and 9 cm.**

Solution:

As we know,

Volume (*V*) = ${\dfrac{1}{3}lwh}$, here l = 9 cm, w = 6 cm, h = 8 cm

∴ V = ${\dfrac{1}{3}\times 9\times 6\times 8}$

= 144 cm^{3}

**Find the volume of a hexagonal pyramid whose height is 7 cm, and base is 3 cm.**

Solution:

As we know,

Volume (*V*) = ${\dfrac{\sqrt{3}}{2}b^{2}h}$ , here b = 3 cm, h = 7 cm

∴ V = ${\dfrac{\sqrt{3}}{2}\times 3^{2}\times 7}$

= 554.55 cm^{3}

Finding the volume of a hexagonal pyramid when the **BASE, APOTHEM, **and **HEIGHT** are known

**Find the volume of a hexagonal pyramid with a height of 14 cm, base of 5 cm, and apothem of 4.3 cm.**

Solution:

Here we will use an alternative formula to calculate the volume.** Volume ( V) = abh, **here a = 4.3 cm, b = 5 cm, h = 14 cm

∴ V = 4.3 × 5 × 14

= 301 cm

**Find the volume of a pentagonal pyramid with a height of 11 cm, base of 7 cm, and apothem of 4.81 cm.**

Solution:

As we know,

Volume (*V*) = ${\dfrac{5}{6}abh}$,** **here a = 4.81 cm, b = 7 cm, h = 11 cm

∴ V = ${\dfrac{5}{6}\times 4.81\times 7\times 11}$

= 308.64 cm^{3}

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

**Find the volume of a pentagonal pyramid with a height of 9.5 cm, and base of 6 cm.**

Solution:

Here we will use an alternative formula to calculate the volume.

Volume (*V*) = ${\dfrac{1.72}{3}b^{2}h}$, here b = 6 cm, h = 9.5 cm

∴ V = ${\dfrac{1.72}{3}\times 6^{2}\times 9.5}$

= 196.08 cm^{3}

**Find the volume of a given truncated pyramid.**

Solution:

Volume (*V*) = ${\dfrac{1}{3}h^{2}\left( a^{2}+b^{2}+ab\right)}$, here a = 10 cm, b = 4 cm, h = 7.5 cm

∴ V = ${\dfrac{1}{3}\times 7.5^{2}\times \left( 10^{2}+4^{2}+10\times 4\right)}$

= 390 cm^{3}

Last modified on August 3rd, 2023