Let’s learn how to determine the volume of a pyramid.
What is a Pyramid?
A pyramid is a three-dimensional solid with a polygonal base and triangular faces that intersect at a point called the apex (or vertex). Pyramids are classified according to the shape of their base.
Regular pyramids, unsurprisingly, have bases that are regular polygons. Examples are triangular pyramids and square pyramids. In contrast, irregular pyramids have irregular polygons (shapes with unequal sides and angles) as bases. Then there are also oblique and right pyramids.
How to Find the Volume of a Pyramid:
No matter the type, there’s only one way to get the volume of a pyramid. Recall that volume refers to the amount of space an object occupies. It is measured in cubic units, such as cm3, m3, and in3. Make sure all units are the same before you look for any object’s volume.
The volume of a pyramid is one-third the area of its base and its height (not slant height), as expressed in the formula:
V = (1 / 3) B h
where V = Volume; B = Area of the Pyramid’s Base; h=Height of the Pyramid.
Related Reading: Volume of a Cone – Formula & Examples
Example #1:
Find the base and volume of a square pyramid with 8cm sides and 12cm height.
Solution for Example #1: Finding the Volume of a Square Pyramid
Step 1. Write the given figures. The pyramid’s base is a square with 8cm sides, so compute its area by multiplying 8cm by 8cm (recall: the area of a square equals side times side).
B = (8cm) (8cm) = 64cm2
Step 2. Plug the measurements (B = 64cm2, h = 12cm) into the formula for volume, then simplify.
V = (1 / 3) B h
V = (1 / 3) (64cm2) (12cm)
= (1 / 3) (768cm3)
V = 256cm3
Therefore, the volume of the pyramid is 256cm3.
Example #2: Finding the Volume of a Rectangular Pyramid
Find the volume of a pyramid with a height of 10cm and a rectangular base measuring 7cm by 3cm.
Solution for Example #2:
Step 1. Find the value of the area of the rectangular base.
Recall that the area of a rectangle is the product of its length and width, which are 7cm and 3cm.
B = l w
= (7cm) (3cm)
B = 21cm2
Step 2. Substitute the measurements (B = 21cm2, h = 10cm) into the formula for volume, then simplify.
V = (1 / 3) B h
V = (1 / 3) (21cm2) (10cm)
= (1 / 3) (210cm3)
V = 70cm3
Therefore, the volume of the pyramid is 70cm3.
Example #3: Finding the Volume of a Triangular Pyramid
Find the volume of a pyramid with a height of 16cm and a right triangle base measuring 9cm by 13cm.
Solution for Example #3:
Step 1: Calculate the value of B by finding the area of the right triangle.
Recall that the area of a triangle is half the product of its base and height.
Note that the triangular base’s height is different from the pyramid’s overall height, which is h = 16cm.
B = (1 / 2) b h
= (1 / 2) (9cm) (13cm)
= (1 /2) (117cm2)
B = 58.5cm2
Step 2. Substitute 58.5cm2 for B and 16cm for h in the volume formula, then simplify.
V = (1 / 3) B h
V = (1 / 3) (58.5cm2) (16cm)
= (1 / 3) (936cm3)
V = 312cm3
Therefore, the volume of the pyramid is 312cm3.
Thank you for reading. We hope it’s effective! Always feel free to revisit this page if you ever have any questions about the volume of a pyramid.
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