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Summary of important concepts

Volume of Prisms

Solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units.

Every prism works the same way: find the area of the flat end, then push it along. One idea covers rectangular prisms, triangular prisms and beyond.

Builds onYr 7 · Area of Triangles and Parallelograms

Method

The universal rule
V=Across-section×lengthV = A_{\text{cross-section}} \times \text{length}
Area of the end face, times how long it is.
Rectangular prism
V=lwhV = lwh
Just the general rule with a rectangle as the end.
Units are cubic
cm3, m3\text{cm}^3,\ \text{m}^3
Three dimensions multiplied means three little marks.

Worked example

e.g. Find the volume of a triangular prism whose end has base 6 cm and height 4 cm, and which is 10 cm long.\text{Find the volume of a triangular prism whose end has base } 6\text{ cm and height } 4\text{ cm, and which is } 10\text{ cm long.}
  1. Identify the cross-section — the shape of the flat end.a triangle\text{a triangle}
  2. Find its area.A=12×6×4=12A = \tfrac{1}{2} \times 6 \times 4 = 12
  3. Write the volume rule.V=A×lengthV = A \times \text{length}
  4. Substitute.V=12×10V = 12 \times 10
  5. Answer with cubic units.V=120 cm3V = 120\text{ cm}^3

Practice

Find the cross-section area first, then multiply by the length.

1
Rectangular prism 5×3×4\text{Rectangular prism } 5\times3\times4
Answer60 cm360\text{ cm}^3
2
Triangular prism, end area 15, length 8\text{Triangular prism, end area } 15, \text{ length } 8
Answer120 cm3120\text{ cm}^3
3
Cube of side 4\text{Cube of side } 4
Answer64 cm364\text{ cm}^3
4
A prism has volume 90 and length 9. Find the end area.\text{A prism has volume } 90 \text{ and length } 9. \text{ Find the end area.}
Answer10 cm210\text{ cm}^2
5
Why is the unit cm3 and not cm2?\text{Why is the unit cm}^3 \text{ and not cm}^2?
AnswerThree lengths are multiplied, not two.\text{Three lengths are multiplied, not two.}
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