The volume of prism is 1920√3 cm^3?. If the base
of the triangle is 16 cm. Then the height of the
prism is.
Answers
Step-by-step explanation:
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