Calculation of Prism Volume
Table of Contents
Volume of a Prism
The volume of a prism is the area of the base multiplied by the height/length. A prism is a solid object with identical ends, flat faces and has the same cross-section along its length (cylinders are not prisms).
There are different types of prisms such as triangular, rectangular and irregular prisms. We also have right prisms (bases on either end are perfectly aligned) and we have oblique prisms where the faces are not aligned.
Calculating volumes are common mathematics exam questions and it is important to know during any stage of your studies (i.e, high school to university). As a former engineering student, it is important to know the volumes of shapes.
This article will go over volume examples of triangular right prisms.
A prism is a solid object with identical ends, flat faces and has the same cross-section along its length. (cylinders are not prisms)
In this shape, the area of the base at both ends are identical, giving 2B (B is base area)
B = area of base, , h = height
The volume of a prism formula is the area of base (B) multiplied by the length (h).
Volume = B*h
Formula for volume of a Prism = B*h
Volume of a Prism Example 1
A prism has an a base area of 38.25 cm2 and a length of 15 cm. What is the volume of the prism?
Solution:
The prism volume formula is B*h
B (area of one end) = 38.25 cm2
H (length/height of prism) = 15cm
Prism Volume = 38.25*15 = 574 cm2
This can also be written as 0.000574 m2 (574 multiplied by 10-6 to convert from cm3 to m3).
Note – remember to check units when calculating the volume.
Volume of a Prism Example 2
A prism has an a side lengths of 1000mm, 713mm, 800mm and height of 566mm. The height/length of the prism is 1000mm. What is the volume of the prism?
Solution:
The prism volume formula is B*h
B (area of one end) =0.5*1000*566 = 283,000 mm2 (area of a triangle)
H (length/height of prism) = 1000 mm
Prism Volume = 283,000*1000 = 283,000,000 mm3
This can also be written as 3.079 m2 (283,000,000 multiplied by 10-9 to convert from mm3 to m3).
Note – remember to check units when calculating the volume.
Prism examples in real life
Everyday examples of prisms include rectangular tissue boxes, cereal boxes, houses and skyscrapers.
Triangular prism examples include triangular roofs, camping tents and even chocolate bars (Toblerone).
There are even hexagonal prisms (have eight faces with two hexagonal bases and six rectangular sides) and these include nuts and bolts.