How to Calculate the Volume of a Square Pyramid
Measure the side length of the base., Calculate the area of the base., Multiply the area of the base by the pyramid's height., Divide this answer by 3.
Step-by-Step Guide
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Step 1: Measure the side length of the base.
Since, by definition, square pyramids have bases that are perfectly square, all of the sides of the base should be equal in length.
Thus, for a square pyramid, you only need to find the length of one side.Consider a pyramid whose base is a square with side lengths of s=5cm{\displaystyle s=5{\text{cm}}}.
This is the value you will use to find the area of the base.
If the sides of the base are not equal in length, you have a rectangular pyramid rather than a square pyramid.
The volume formula for rectangular pyramids is very similar to the formula for square pyramids.
If l{\displaystyle l} represents the length of the rectangular pyramid's base and w{\displaystyle w} represents its width, the pyramid's volume is V=13h∗l∗w{\displaystyle V={\frac {1}{3}}h*l*w}. -
Step 2: Calculate the area of the base.
Finding the volume begins by finding the two-dimensional area of the base.
This is done by multiplying the base's length times its width.
Because the base of a square pyramid is a square, its sides all have equal lengths, so the area of the base is equal to the length of one side squared (times itself).In the example, since the side lengths of the pyramid's base are all 5 cm, you can find the base's area as: area=s2=(5cm)2=25cm2{\displaystyle {\text{area}}=s^{2}=(5{\text{cm}})^{2}=25{\text{cm}}^{2}} Remember that two-dimensional areas are expressed in square units
- square centimeters, square meters, square miles, and so on. , Next, multiply the base area by the height of the pyramid.
As a reminder, the height is the distance of the line segment stretching from the apex of the pyramid to the plane of the base at perpendicular angles to both.In the example, suppose the pyramid has a height of 9 cm.
In this case, multiply the area of the base by this value as follows: 25cm2∗9cm=225cm3{\displaystyle 25{\text{cm}}^{2}*9{\text{cm}}=225{\text{cm}}^{3}} Remember that volumes are expressed in cubic units.
In this case, because all the linear measurements are centimeters, the volume is in cubic centimeters. , Finally, find the volume of the pyramid by dividing the value you just found from multiplying the base area by the height by
3.
This will give you a final answer that represents the volume of the square pyramid.In the example, divide 225 cm3 by 3 to get an answer of 75 cm3 for the volume. -
Step 3: Multiply the area of the base by the pyramid's height.
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Step 4: Divide this answer by 3.
Detailed Guide
Since, by definition, square pyramids have bases that are perfectly square, all of the sides of the base should be equal in length.
Thus, for a square pyramid, you only need to find the length of one side.Consider a pyramid whose base is a square with side lengths of s=5cm{\displaystyle s=5{\text{cm}}}.
This is the value you will use to find the area of the base.
If the sides of the base are not equal in length, you have a rectangular pyramid rather than a square pyramid.
The volume formula for rectangular pyramids is very similar to the formula for square pyramids.
If l{\displaystyle l} represents the length of the rectangular pyramid's base and w{\displaystyle w} represents its width, the pyramid's volume is V=13h∗l∗w{\displaystyle V={\frac {1}{3}}h*l*w}.
Finding the volume begins by finding the two-dimensional area of the base.
This is done by multiplying the base's length times its width.
Because the base of a square pyramid is a square, its sides all have equal lengths, so the area of the base is equal to the length of one side squared (times itself).In the example, since the side lengths of the pyramid's base are all 5 cm, you can find the base's area as: area=s2=(5cm)2=25cm2{\displaystyle {\text{area}}=s^{2}=(5{\text{cm}})^{2}=25{\text{cm}}^{2}} Remember that two-dimensional areas are expressed in square units
- square centimeters, square meters, square miles, and so on. , Next, multiply the base area by the height of the pyramid.
As a reminder, the height is the distance of the line segment stretching from the apex of the pyramid to the plane of the base at perpendicular angles to both.In the example, suppose the pyramid has a height of 9 cm.
In this case, multiply the area of the base by this value as follows: 25cm2∗9cm=225cm3{\displaystyle 25{\text{cm}}^{2}*9{\text{cm}}=225{\text{cm}}^{3}} Remember that volumes are expressed in cubic units.
In this case, because all the linear measurements are centimeters, the volume is in cubic centimeters. , Finally, find the volume of the pyramid by dividing the value you just found from multiplying the base area by the height by
3.
This will give you a final answer that represents the volume of the square pyramid.In the example, divide 225 cm3 by 3 to get an answer of 75 cm3 for the volume.
About the Author
Michael Adams
Committed to making crafts accessible and understandable for everyone.
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