# Volume of prisms

## Discovering the Potential of Prisms and How to Find Their Volume

If you've ever wondered about the holding capacity of different shapes, then you'll be interested to know how to determine their volume. In this article, we will dive into the world of prisms and their varying capacities.

So, what is a prism exactly? A prism is a solid object with two identical and opposing surfaces that can be repositioned to face sideways. The shape of the prism's base can differ, with common types including rectangular, triangular, trapezoidal, square, and hexagonal.

To calculate the volume of a prism, you'll need to know the base area and height. The formula for finding the volume of a prism is to multiply the base area by the height. Let's take a look at some direct formulas for calculating the volume of different prisms.

Rectangular Prism: Also known as a cuboid, a rectangular prism has a rectangular base. To find its volume, we use the formula V = lwh, where l is the length, w is the width, and h is the height. For example, if a matchbox has a length of 12 cm, a width of 8 cm, and a height of 5 cm, its volume can be calculated as follows: V = (12 cm) x (8 cm) x (5 cm) = 480 cm³

Triangular Prism: A triangular prism has similar triangles for its top and base. Its volume can be calculated using the formula V = ½ x b x h, where b is the base length and h is the height. For instance, if a triangular prism has a base length of 10 m, a height of 9 m, and a depth of 6 cm, its volume can be found using the following steps: V = ½ x (10 m) x (9 m) x (6 cm) = 270 m³

Square Prism: Also called a cube, a square prism has equal sides and a square base. Its volume can be calculated using the formula V = s³, where s is the length of one side. For example, if a cube has a side length of 5 cm, its volume can be found using the following formula: V = (5 cm)³ = 125 cm³

Trapezoidal Prism: A trapezoidal prism has a trapezoidal base on both ends. Its volume is the product of the base area and the prism's height. The formula for the area of a trapezium is A = ½ x (a + b) x h, where a and b are the lengths of the parallel sides and h is the height. For instance, if a sandwich box has a trapezoidal base with top breadth length of 5 cm, bottom breadth length of 8 cm, and a height of 6 cm, and a depth of 3 cm, its volume can be calculated as follows: V = (½ x (5 cm + 8 cm) x (6 cm)) x (3 cm) = 65 cm³

Hexagonal Prism: A hexagonal prism has a hexagonal base and equal sides. Its volume is the product of the base area and the prism's height. The formula for the area of a regular hexagon is A = 3√3/2 x s², where s is the length of one side. For example, if a hexagonal prism has a side length of 7 cm and a height of 5 cm, its volume can be calculated as follows: V = (3√3/2 x (7 cm)²) x (5 cm) = 193.3 cm³

In summary, the volume of a prism can be found by multiplying the base area and the height. By knowing the direct formulas for different types of prisms, we can easily calculate their volumes. These calculations have numerous practical applications, making them useful for determining the volume of various shapes.

## Understanding Capacity: How Prisms Determine Volume

When it comes to measuring capacity, it's important to note that it is typically measured in cubic units, such as cubic centimeters or cubic meters. However, to better understand this measurement, we can convert it to a more familiar unit, such as liters, by using a conversion factor.

In order to determine the capacity of a figure, we must first calculate the volume of each individual prism within the figure. Once we have the total volume, we can then convert it to our desired unit of measurement. By grasping the basic concept of prisms and their volume calculation, we can easily determine the capacity of any figure. This knowledge becomes especially useful when trying to gauge how much a container can hold.