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Volume of PyramidVolume 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.
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} _____________________________________________________________________ 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} _____________________________________________________________________ 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 Home Page
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