# Volume of Pyramid

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Volume of Pyramid : (Pyramid ) : There are different types of pyramid, depending on their bases. If the base is triangle then it is called triangular pyramid . If base is rectangle then it is called as rectangular pyramid and so on. 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

From Pyramid to Mensuration