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Square Base Pyramid Volume Calculator
Welcome to our Square Base Pyramid Volume Calculator page.
We explain how to find the volume of a square pyramid and provide a quick calculator to work it out for you, step-by-step.
There are also some worked examples and some worksheets for you to practice this skill.
Quicklinks to ...
Square Base Pyramid Volume Calculator
This calculator finds the volume of a right square pyramid when the base length and perpendicular height are known.
How the Square Base Pyramid Volume Calculator Works
- Type in the value for the width of the edge of the base (b).
- Type in a value for the height of the square pyramid (h).
- For each value, you can choose a whole number, decimal or fraction.
- You can type a fraction by typing the numerator then '/' then the denominator.
- You can type a mixed number by typing the whole-number part, then a space then the fraction part.
- Examples: 2 1/2 (two and one-half); 3 4/5 (three and four-fifths); 7 1/3 (seven and one-third).
- Choose your units of measurement (default is none)
- Choose your desired accuracy (default is 2 decimal places)
- Click the Find Volume button
Volume of a Square Base Pyramid Formula
The volume of a right square pyramid is: \[ V = {1 \over 3} b^2 h \]
where b is the width of the edge of the square base and h is the perpendicular height of the pyramid.
Square Base Pyramid Volume Examples
Volume of a Square Base Pyramid Example 1
Find the volume of the square base pyramid below.
The formula for the volume of a square base pyramid is: \[ V = {1 \over 3} b^2 h \]
If we substitute the values of the base width and height into this equation, we get: \[ A = {1 \over 3} \cdot 6^2 \cdot 8 = {1 \over 3} \cdot 36 \cdot 8 = {1 \over 3} \cdot 288 = 96 \]
This gives us a final answer of: \[ V = 96 \;\ cm^3 \]
Volume of a Square Base Pyramid Example 2
Find the volume of the square base pyramid below.
The formula for the volume of a square base pyramid is: \[ V = {1 \over 3} b^2 h \]
If we substitute the values of the base edge and height into this equation, we get: \[ A = {1 \over 3} \cdot (3 {1 \over 2})^2 \cdot 6 = {1 \over 3} \cdot {39 \over 4} \cdot 6 = {1 \over 3} \cdot {147 \over 2} = {49 \over 2} \]
This gives us a final answer of: \[ V = 24.5 \;\ in^3 \]
Volume of a Square Base Pyramid Example 3
Find the volume of the square base pyramid below. Give your answer correct to 2 decimal places.
The formula for the volume of a square base pyramid is: \[ V = {1 \over 3} b^2 h \]
If we substitute the values of the base edge and height into this equation, we get: \[ A = {1 \over 3} \cdot (2.3)^2 \cdot 6.4 = {1 \over 3} \cdot 5.29 \cdot 6.4 = {1 \over 3} \cdot 33.856 = 11.285333... \]
This gives us a final answer of: \[ V = 11.29 \;\ cm^3 \; to \; 2 \; decimal \; places \]
Volume of a Square Base Pyramid Example 4
A giant model bird has a beak which is made up of a square base pyramid on its side. Find the volume of the beak.
The formula for the volume of a square base pyramid is: \[ V = {1 \over 3} b^2 h \]
If we substitute the values of the base edge and height into this equation, we get: \[ A = {1 \over 3} \cdot (1.2)^2 \cdot 2.6 = {1 \over 3} \cdot 1.44 \cdot 2.6 = {1 \over 3} \cdot 4.032 = 1.248 \]
This gives us a final answer of: \[ V = 1.248 \;\ m^3 \; \]
Volume of a Square Base Pyramid Worksheets
We have created two worksheets to help you practice this skill.
The first sheet involves working out the volume of a range of square base pyramids in the same orientation.
The second sheet involves working out the volume of square base pyramids in different orientations and where some redundant measurements are included.
You can check your answers to the questions on the sheets using our square base pyramid volume calculator.
More Recommended Math Resources
Take a look at some more of our worksheets similar to these.
More Area & Volume Calculators
We have a range of area and volume calculators to help you find the area and volumes of a range of different 2d and 3d shapes.
Each calculator page comes with worked examples, formulas and practice worksheets.
More Area Support and Resources
We have a range of other area worksheets and support pages for a range of different 2d shapes.
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