Volume of Prisms

Concept

The volume of a prism is the capacity of the prism. There can be different types of prisms like a triangular prism, square prism, rectangular prism, pentagonal prism, hexagonal prism, or octagonal prism. But the method to write the formula of volume of any prism remains the same immaterial of the type of prism. The concept of writing the formula for the volume of the prism stays the same in any case.

Rules

The formula for the volume of a prism is given by the product of the area of the base and height of the prism.
Thus, the volume of a prism can be given as V = B × H where V is the volume, B base area, and H height of the prism. The unit of base area is given in square units and the height of the prism is given in units. Thus, the unit of volume of the prism is given as:
V = (square units) × (units) = cubic units.
Volume of Rectangular Prisms: L x W x H
Volume of Triangular Prisms: $\fn_phv (\frac{1}{2}\times base\times height) \times height\; of\; prism$

Example

Find the volume of the prism.

Solution

V = base area × height

V = $\fn_phv \frac{1}{2}\times base \times height \times length\;of\;the\;prism$

V = $\fn_phv \frac{1}{2}\times 0.9\;m\times 1.2\;m \times 3.8\;m$

V = 2.052 ≈ 2.1 m³

Practice Volume of Prisms

Practice Problem 1

What is the volume of the prism?

Practice Problem 2

What is the volume of the prism?

Practice Problem 3

A rectangular flower pot is 16 cm length, 5.2 cm width, and $\fn_phv {\color{Teal} 10\frac{1}{2}}$ cm height. What is the volume of the pot?

Practice Problem 4

Sally is buying yogurt. Which container will hold more yogurt?

Volume: It is the measure of the space occupied by a solid. Volume is measured in cubic units.

Prism: A prism is a three-dimensional solid which has identical faces at both ends. The other faces are flats. A prism is named after its base.

Rectangular Prism: A solid (3-dimensional) object which has six faces that are rectangles. It has the same cross-section along a length, which makes it a prism.

Triangular Prism: A triangular prism is a polyhedron, made up of two triangular bases and three rectangular sides

Pre-requisite Skills
Measurement – Area
Area of a triangle
Volume of Rectangular Prisms