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Wize High School Geometry Textbook (Common Core) > 3D Measurements

Surface Area & Volume of a Prism

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Prisms

What do these objects have in common?


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A prism is a solid 3D object that has the same end faces, and the same cross-section along its length.

Common Prisms



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Surface Area of a Prism

The surface area of a prisms is the total area you get by adding up the area of each face of the prism.
  • Surface area is measured in unit2 (commonly cm2, m2, inch2, feet2, etc.)

Example
The surface area of this prism is
  • Front face: 3×2=6m23\times2=6 m^2
  • Back face: 3×2=6m23\times 2=6 m^2
  • Top face: 3×5=15m23\times 5=15m^2
  • Bottom face: 3×5=15m23\times 5=15m^2
  • Left face: 2×5=10m22\times 5 =10m^2
  • Right face: 2×5=10m22\times 5 =10m^2
In total, the surface area of this prism is 6+6+15+15+10+10=62m26+6+15+15+10+10=62m^2

Practice: Surface Area of a Prism

What is the surface area of the following cube?

Practice: Surface Area of a Prism

What is the surface area of the following prism?


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Volume of a Prism

The volume of a prisms is the total "space" occupied by the prism, and it is calculated using this formula:
Vprism=(Area of the base)×height\large\boxed{V_\text{prism}=(\text{Area of the base})\times \text{height}}
  • Volume is measured in unit3 (commonly cm3, m3, inch3, feet3, etc.)
  • Volume can also be measured in ml, L, etc.

Example
The volume of this prism is
V=(Area of the base)×heightV=(l×w)×hV=(3×2)×5V=30 m2\begin{array}{rcl} V&=&(\text{Area of the base})\times\text{height}\\ V&=&(l\times w)\times h\\ V&=&(3\times2)\times 5\\ V&=&30~m^2 \end{array}
So, the volume of this prism is 30 m2

Practice: Volume of a Prism

Find the volume of this cube.

Practice: Volume of a Prism

What is the volume of this triangular-based prism?


Practice: Prisms

Joe is designing a box for his chocolate company. He wants the box to be a prism with a regular pentagon base as shown in this diagram.

a) If the chocolate box must have a volume of 270 cm3, what should the length of this chocolate box be?

b) The chocolate box will be made out of cardboard material that cost $0.50/cm2. What is the cost required to produce the box from part a)?