Calculate Surface Area of Right Pri...
Calculate Surface Area of Right Prism Given the Volume

Volume of Prism

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

Volume of Prism : Prism:
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 82
⇒ 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 cm3
2) The volume of a prism is 300 and its base is a right triangle. If the area of the base of the triangle is 30 cm2 then find the height of the prism.
Solution: Volume of the prism = 300 ; area of base = 30 cm2
Volume of prism = area of base x height
300 = 30 x h
∴ h = 300 /30 = 10 cm.
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 cm2
Volume of prism = Area of base x H
∴ V = 77.4 x 10
∴ Volume = 774 cm3

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

From Prism to Mensuration

From Prism to Home Page