# Volume of Prism

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

**Apothem :**The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides. The word "apothem" can also refer to the length of that line segment. Regular polygons are the only polygons that have apothems. Because of this, all the apothems in a polygon will be congruent and have the same length.

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) |

**Some solved examples :**

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)

**Solution :**

As the base of triangular prism is equilateral.

∴ Area of base = √ 3 / 4 (side)

^{2}

⇒ Area of base = √3 / 4 x 8

^{2}

⇒ 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

^{3}

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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

^{2}then find the height of the prism.

**Solution:**Volume of the prism = 300 cu.cm ; area of base = 30 cm

^{2}

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.

**Solution:**apothem = A = 4.3 cm and side = 6cm

Perimeter = 6 x 6 = 36 cm

Area of Base (hexagon) = AP /2

⇒ Area = (4.3 x 36 )/2

⇒ Area = 77.4 cm

^{2}

Volume of prism = Area of base x H

∴ V = 77.4 x 10

∴ Volume = 774 cm

^{3}

**Volume :**

• 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

• 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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