![]() ![]() But before we do that, we need to define a few terms.Ī rectangular prism, or rectangular solid, is a 6-sided object where each side, also called a face, is a rectangle. It has 12 edges and eight vertices and all of its angles are right angles.Īn important measure of a rectangular prism is the volume. The volume of a prism or any other 3D object is a measure of how much space it takes up. We measure this in cubic units, such as cubic inches or cubic centimeters. It’s easy to picture this with a rectangular prism. Imagine that we have a bunch of little cubes that are 1 centimeter tall, 1 centimeter wide, and 1 centimeter long. Each one of these cubes is 1 cubic centimeter, which can also be written like this \(1\text^2\). We’ll just know the dimensions of the rectangular prism, like this: This problem lets us see the square centimeters, but most surface area problems won’t show us the squares. The corresponding edges on the opposite sides will be the same since this is a rectangular prism.Volume of Prisms – Explanation & Examples Here we can see our prism is 10 meters long by 5 meters wide by 4 meters high. The volume of a prism is the total space occupied by a prism. In this article, you will learn how to find a prism volume by using the volume of a prism formula.īefore we get started, let’s first discuss what a prism is. ![]() Prisms are named after the shapes of their cross-section.īy definition, a prism is a geometric solid figure with two identical ends, flat faces, and the same cross-section all along its length. For example, a prism with a triangular cross-section is known as a triangular prism. Other examples of prisms include rectangular prism. pentagonal prism, hexagonal prism, trapezoidal prism etc. To find the volume of a prism, you require the area and the height of a prism. The volume of a prism is calculated by multiplying the base area and the height. The volume of a prism is also measured in cubic units, i.e., cubic meters, cubic centimeters, etc. The formula for calculating the volume of a prism depends on the cross-section or base of a prism. The volume of a Prism = Base Area × Length The general formula for the volume of a prism is given as Since we already know the formula for calculating the area of polygons, finding the volume of a prism is as easy as pie. Where Base is the shape of a polygon that is extruded to form a prism. Let’s discuss the volume of different types of prisms. The formula for the volume of a triangular prism is given as Volume of a triangular prismĪ triangular prism is a prism whose cross-section is a triangle. The polygon’s apothem is the line connecting the polygon center to the midpoint of one of the polygon’s sides. ![]() The apothem of a triangle is the height of a triangle.įind the volume of a triangular prism whose apothem is 12 cm, the base length is 16 cm and height, is 25 cm.įind the volume of a prism whose height is 10 cm, and the cross-section is an equilateral triangle of side length 12 cm.įind the apothem of the triangular prism. The volume of a hexagonal prism is given by:Ĭalculate the volume of a hexagonal prism with the apothem as 5 m, base length as 12 m, and height as 6 m.Īlternatively, if the apothem of a prism is not known, then the volume of any prism is calculated as follows Therefore, the apothem of the prism is 10.4 cmįor a pentagonal prism, the volume is given by the formula:įind the volume of a pentagonal prism whose apothem is 10 cm, the base length is 20 cm and height, is 16 cm.Ī hexagonal prism has a hexagon as the base or cross-section. S = side length of the extruded regular polygon. NOTE: This formula is only applied where the base or the cross-section of a prism is a regular polygon.įind the volume of a pentagonal prism with a height of 0.3 m and a side length of 0.1 m.
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