Pre-Algebra
Geometry
Volume of prisms and pyramids
20 practice questions
0 video lessons
Theory + worked examples
Volume of Prisms and Pyramids
California Pre-Algebra • Standard 7.G.6 • Geometry
Volume of Prisms and Pyramids is a topic in Geometry in the California Common Core State Standards. It is aligned to Standard 7.G.6, which requires students to find the volume of prisms and pyramids.
The volume of a prism is the base area times the height; a pyramid is one third of that.
Theory
Volume is the space inside a solid, measured in cubic units.
- Prism: \(V=Bh\), where \(B\) is the base area.
- Pyramid: \(V=\dfrac{1}{3}Bh\).
\(B\) is the area of the base, \(h\) the perpendicular height.
A rectangular prism.
Volume formulas.
Volume:
\[V_{\text{prism}}=Bh,\qquad V_{\text{pyramid}}=\dfrac{1}{3}Bh\]
Volume is in cubic units.
How to find volume
- Find the area of the base \(B\).
- Multiply by the height for a prism.
- Take one third for a pyramid.
- Label in cubic units.
Example 1 — Rectangular prism
Find the volume of a \(4\times3\times5\) prism.
Solution
Base area times height.
| \((4\cdot3)\cdot5\) | \(=\) | \(60\) |
Example 2 — Triangular prism
Base area \(6\), length \(10\). Find the volume.
Solution
Base times length.
| \(6\cdot10\) | \(=\) | \(60\) |
Example 3 — Pyramid
Base area \(12\), height \(5\). Find the pyramid's volume.
Solution
One third base times height.
| \(\dfrac{1}{3}(12)(5)\) | \(=\) | \(20\) |
Example 4 — Units
What units does volume use?
Solution
Cubic units.
Common pitfalls
\(B\) is the base area, not a side length.
Pyramids have the \(\dfrac13\).
Volume is cubed units.
Frequently asked questions
What is volume?
The space inside a solid, in cubic units.
What is a prism's volume?
Base area times height.
What is a pyramid's volume?
One third base area times height.
What units does volume use?
Cubic units.
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