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.
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This calculator finds the volume of a right square pyramid when the base length and perpendicular height are known.
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.
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: \[ V = 96 \;\ cm^3 \]
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: \[ V = 24.5 \;\ in^3 \]
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: \[ V = 11.29 \;\ cm^3 \; to \; 2 \; decimal \; places \]
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: \[ V = 1.248 \;\ m^3 \; \]
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.
Take a look at some more of our worksheets similar to these.
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