# Volume of Pyramid

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Volume of these solids are depending on the area of their bases.

Volume of triangular Pyramid | V = 1/3 x Area of triangular base x height(H) V = 1/3( base x height) / 2 x H |

Volume of Hexagonal Pyramid |
V = 1/3 x Area of hexagon x H V = 6 x (√3 / 4 ) (side) ^{2} x H V = 1/3(AP/ 2) x H ( A = apothem ; P = perimeter) |

Volume of Pentagonal Pyramid | Volume = 1/3 x area of base x height(H) V = 1/3 (AP/ 2) x H ( A = apothem ; P = perimeter) |

**Some solved examples**

1) If the length of each side of the base of a triangular pyramid is 6 cm and its height is 10 cm, find its volume. ( √3 = 1.73)

**Solution :**

Area of base = √3 / 4 x (side)

^{2}

⇒ Area = √3 / 4 x (6)

^{2}

⇒ Area = √3 /4 x 36

∴ Area = 9 √3 cm

^{2}

Pyramid volume = 1/3 x area of base x height

⇒ Pyramid volume = 1/3 x 9 √3 x 10

⇒ Volume = 30 √3

⇒ Volume = 30 x 1.73

⇒ Volume = 51.9 cm

^{3}

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2) If the length of each side of a square pyramid is 4 cm and its height is 12 cm.

**Solution :**

Area of base = side x side

⇒ Area = 4 x 4

⇒ Area = 16 cm

^{2}

Pyramid volume = 1/3 x area of base x height

⇒ Volume = 1/3 x 16 x 12

⇒ Volume = 64 cm

^{3}

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3) Find the volume of a regular hexagonal pyramid with an apothem length of 6 cm,

side 3 cm and height of the pyramid is 21 cm.

**Solution :**

apothem = A = 6 cm and side = 3 cm height = H =21 cm

Perimeter = 3 x 6 = 18 cm

Area of Base (hexagon) = AP /2

⇒ Area = (6 x 18 )/2

⇒ Area = 54 cm

^{2}

volume of pyramid=1/3 x( Area of base) x H

∴ V = 1/3 x 54 x 21

∴ Volume = 378 cm

^{3}

**Volume :**

• Volume Formulas

• Volume of Irregular Shape

• Volume of Cube

• Volume of Rectangular Prism(Cuboid)

• Volume of Cylinder

• Cone volume

• Sphere's volume

• Hemisphere's volume

• Prism's volume

• Volume of Pyramid

• Volume Formulas

• Volume of Irregular Shape

• Volume of Cube

• Volume of Rectangular Prism(Cuboid)

• Volume of Cylinder

• Cone volume

• Sphere's volume

• Hemisphere's volume

• Prism's volume

• Volume of Pyramid

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