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Volume of Prism : Prism:There are different types of prism. Such as Triangular prism,Hexagonal Prism and Pentagonal prism.

Here, OA is an apothem of regular hexagon.

The formula to find the volume different is similar.

Volume of triangular Prism | V = Area of triangular base x height(H) V = ( base x height) / 2 x H |

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

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

1) The base of a triangular prism is an equilateral triangle with side 8 cm. Its height is 10 cm. Find the volume of the prism.( √ 3 = 1.73)

As the base of triangular prism is equilateral.

∴ Area of base = √ 3 / 4 (side)

⇒ Area of base = √3 / 4 x 8

⇒ Area = 16 √3

⇒ Area = 16 x 1.73 = 27.68

Volume of prism = Area of base x height

V= 27.68 x 10

Volume = 276.8 cm

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2) The volume of a prism is 300 cu.cm and its base is a right triangle. If the area of the base of the triangle is 30 cm

Volume of prism = area of base x height

300 = 30 x h

∴ h = 300 /30 = 10 cm.

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3) Find the volume of a regular hexagonal prism with an apothem length of

4.3 cm ,side 6cm and height of the prism is 10 cm.

Perimeter = 6 x 6 = 36 cm

Area of Base (hexagon) = AP /2

⇒ Area = (4.3 x 36 )/2

⇒ Area = 77.4 cm

Volume of prism = Area of base x H

∴ V = 77.4 x 10

∴ Volume = 774 cm

• Volume Formulas

• Volume of Irregular Shape

• Volume of Cube

• Volume of Rectangular Prism(Cuboid)

• Volume of Cylinder

• Volume of Cone

• Volume of Sphere

• Volume of Hemisphere

• Volume of Prism

• Volume of Pyramid

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