A prism is a solid geometric figure with two identical base ends and all flat faces. The prism gets its name from its base: for example, if it is a triangle, the solid is called a "triangular prism". To find the volume of a prism, you just have to calculate the area of its base - the most complex part of the whole process - and multiply it by the height. Here's how to calculate the volume of a set of prisms.
Steps
Method 1 of 5: Calculate the Volume of a Triangular Prism
Step 1. Write down the formula for finding the volume of a triangular prism
The formula is simply V = 1/2 x length x width x height.
However you can also use this: V = base area x solid height.
The area of a triangle is found by multiplying 1/2 of the base by the height.
Step 2. Find the area of the base face
To calculate the volume of a triangular prism, it is necessary to first find the area of the base, as indicated in the previous point.
Example: If the height of the triangular base is 5cm and the base is 4cm, then the base area is 1/2 x 5cm x 4cm, which is 10cm2.
Step 3. Find the height
Suppose the height of this triangular prism is 7 cm.
Step 4. Multiply the area of the triangular base by the height and you have the volume of the triangular prism
Example: 10 cm2 x 7 cm = 70 cm3.
Step 5. Put your answer in cubic units
You must always use cubic units when calculating volume, because you are working with three-dimensional objects. The final answer is 70 cm3.
Method 2 of 5: Calculate the Volume of a Cube
Step 1. Write the formula to find the volume of a cube
The formula is simply V = edge3.
A cube is a prism having three equal dimensions.
Step 2. Find the length of an edge of the cube
All edges are the same, so it doesn't matter which one you choose.
Example: Edge = 3 cm
Step 3. Cube it:
just multiply the number by itself, finding the square, and once again by itself. The cube of "a" is "a x a x a", for example. Since all dimensions of the cube are equal, multiplying any two edges will give you the area of the base, and any third edge could represent the height of the solid.
Example: 3 cm3 = 3cm * 3cm * 3cm = 27cm3.
Step 4. Put your answer in cubic units:
the final result is 125 cm3.
Method 3 of 5: Calculate the Volume of a Rectangular Prism
Step 1. Write the formula for finding the volume of a rectangular prism
The formula is simply V = length x width x height.
A rectangular prism is characterized by a base rectangle.
Step 2. Find the length
Length is the longest side of the rectangle on the top or bottom face of the solid.
Example: Length = 10 cm
Step 3. Find the width
The width of the rectangular prism is the smaller side of the base rectangle.
Example: Width = 8 cm
Step 4. Find the height
The height is the part of the rectangular prism that rises. The height of the rectangular prism can be imagined as the part that extends a rectangle placed in a plane and makes it three-dimensional.
Example: Height = 5 cm
Step 5. Multiply the length, width and height
You can multiply them in any order to get the same result. Using this method, you essentially find the area of the rectangular base (10 x 8) and report it as many times as expressed by the height (5).
Example: 10cm x 8cm x 5cm = 400cm3
Step 6. Put your answer in cubic units
The final answer is 400 cm3
Method 4 of 5: Calculate the Volume of a Trapezoidal Prism
Step 1. Write the formula to calculate the volume of a trapezoidal prism
The formula is: V = [1/2 x (base1 + base2) x height] x height of the solid.
You must use the first part of this formula to find the base area, a trapezoid, before continuing.
Step 2. Calculate the area of the trapezoid
To do this, simply substitute the two bases and the height of the trapezoidal base in the first part of the formula.
- Let's assume that basis1 = 8 cm, base2 = 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 it is 12 cm.
Step 4. Multiply the base area by the height
80 cm2 x 12 cm = 960 cm3.
Step 5. Put your answer in cubic units
The final answer is 960 cm3.
Method 5 of 5: Calculate the Volume of a Regular Pentagonal Prism
Step 1. Write the formula to find the volume of a regular pentagonal 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 pentagon. It involves finding the area of five triangles that make up a regular polygon. The side is simply the width of a triangle, while the apothem is the height of one of the triangles. Multiply by 1/2 to find the area of a triangle and then multiply this result by 5, because they are the 5 triangles that make up the pentagon.
To find the apothem using trigonometric formulas, you can do further research
Step 2. Calculate the area of the pentagon
Suppose the side is 6 cm and the length of the apothem is 7 cm. Just enter these numbers into the formula:
- A = 1/2 x 5 x side x apothem
- A = 1/2 x 5 x 6cm x 7cm = 105cm2.
Step 3. Find the height of the prism
Suppose it is 10 cm.
Step 4. Multiply the area of the pentagonal base by the height to find the volume:
105 cm2 x 10 cm.
105 cm2 x 10 cm = 1, 050 cm3.
Step 5. Specify your answer in units per cube
The final answer is 1.050 cm3.
