A prism is a solid geometric shape with two identical parts and all sides are flat. This prism is named after the shape of its base, so a prism with a triangular base is called a triangular prism. To find the volume of a prism, you just need to calculate the area of the base and multiply it by the height – calculating the area of the base can be the tricky part. Here's how to calculate the volume of various prisms. Volume and capacity are almost the same but this is a way of calculating the volume of a prism.
Step
Method 1 of 5: Calculating the Volume of a Triangular Prism
Step 1. Write down the formula to find the volume of a triangular prism
The formula is just V = 1/2 x length x width x height.
However, we will break down this formula to use the formula V = area of base x height.
You can find the area of the base by using the formula for finding the area of a triangle – multiplying 1/2 by the length of the base and the height of the triangle.
Step 2. Find the area of the base
To calculate the volume of a triangular prism, you must first find the area of the base of the triangle. Find the area of the base of the prism by multiplying 1/2 by the length of the base times the height of the triangle.
Example: If the height of the base of a triangle is 5 cm and the length of the base of a triangular prism is 4 cm, then the area of the base is 1/2 x 5 cm x 4 cm, which is 10 cm2.
Step 3. Find the height
Suppose the height of this triangular prism is 7 cm.
Step 4. Multiply the area of the base of the triangle by its height
Just multiply the area of the base by the height. Once you multiply the area of the base and the height, you'll get the volume of a triangular prism.
Example:10 cm2 x 7 cm = 70 cm3
Step 5. Write your answer in cubic units
You should always use cubic units when calculating volume because you are working with three-dimensional objects. The final answer is 70 cm. 3.
Method 2 of 5: Calculating the Volume of a Cube
Step 1. Write down the formula to find the volume of a cube
The formula is only V = side3.
A cube is a prism that happens to have three equal sides.
Step 2. Find the length of one side of the cube
All the sides are the same length, so it doesn't matter which side you choose.
Example: Length = 3 cm
Step 3. To the power of three
To triple a number, simply multiply that number by itself twice. For example, the cube of a is a x a x a. Since all the side lengths of a cube are the same length, you don't need to find the area of the base and multiply it by the height. Multiplying two sides of any cube will give the area of the base and the third side will be the height. You can still think of it as multiplying the length, width, and height by a length that happens to be the same.
Example: 3cm3 = 3cm * 3cm * 3cm = 27cm.3
Step 4. Write your answer in cubic units
Don't forget to write your answer in cubic units. The final answer is 27 cm.3
Method 3 of 5: Calculating the Volume of a Rectangular Prism
Step 1. Write down the formula to find the volume of a rectangular prism
The formula is just V = length * width * height.
A rectangular prism is a prism with a rectangular base.
Step 2. Find the length
Length is the longest side of the rectangular flat surface at the top or bottom of the rectangular prism.
Example: Length = 10 cm
Step 3. Find the width
The width of a rectangular prism is the shortest side of the flat surface at the top or bottom of the rectangular prism.
Example: Width = in 8 cm
Step 4. Find the height
Height is the vertical part of the rectangular prism. You can imagine the height of a rectangular prism as the part that extends from a flat rectangle and makes it three-dimensional.
Example: Height = 5 cm
Step 5. Multiply the length, width, and height
You can multiply all three in any order to get the same answer. Using this method, you will find the area of the base of the rectangle (10 x 8) and multiply it by the height, 5. But to find the volume of this prism, you can multiply the lengths of the sides in any order.
Example: 10cm * 8cm * 5cm = 400cm.3
Step 6. Write your answer in cubic units
The final answer is 400 cm.3
Method 4 of 5: Calculating the Volume of a Trapezoidal Prism
Step 1. Write down the formula for calculating the volume of a trapezoidal prism
The formula is: V = [1/2 x (base1 + pedestal2) x height] x height of the prism.
You should use the first part of the formula to find the area of the base of the trapezoid from the base of the prism before moving on.
Step 2. Find the area of the base of the trapezoid
To do this, just plug the two bases and the height of the trapezoid into the formula.
- Let's say base 1 = 8 cm, base 2 = 6 cm, and height = 10 cm.
- Example: 1/2 x (6 + 8) x 10 = 1/2 x 14 cm x 10 cm = 80 cm2.
Step 3. Find the height of the trapezoidal prism
Suppose the height of the trapezoidal prism is 12 cm.
Step 4. Multiply the area of the side of the base by its height
To calculate the volume of a trapezoidal prism, simply multiply the area of the base side by its height.
80 cm2 x 12cm = 960cm3.
Step 5. Write your answer in cubic units
The final answer is 960 cm3
Method 5 of 5: Calculating the Volume of a Regular Triangular Prism
Step 1. Write down the formula to find the volume of a regular pentagon prism
The formula is V = [1/2 x 5 x side x apothem] x height of the prism.
You can use the first part of the formula to find the area of the base of a pentagon. You can think of it like finding the area of five triangles that make up a regular pentagon. Its side is the width of one of the triangles and its apothem is the height of one of the triangles. You'd multiply by 1/2 because that's part of finding the area of the triangle and then multiplying by 5 because 5 triangles form a pentagon.
For more information on finding the apothem if it is not known, see here
Step 2. Find the area of the base of the pentagon
Suppose the length of the side is 6 cm and the length of the apothem is 7 cm. Plug these numbers into the formula:
- A = 1/2 x 5 x side x apothem
- A = 1/2 x 5 x 6 cm x 7 cm = 105 cm2
Step 3. Find the height
Suppose the height of the shape is 10 cm.
Step 4. Multiply the area of the base of the pentagon by its height
Just multiply the area of the base of the pentagon, 105 cm2, with a height, 10 cm, to find the volume of a regular pentagonal prism.
105 cm2 x 10 cm = 1050 cm3
Step 5. Write your answer in cubic units
The final answer is 1050 cm3.
