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Calculate the volume of prisms

Volume of a prism represents the amount of three-dimensional space it occupies, measured in cubic units, and is calculated as V=BhV=Bh, where BB is the area of a base and hh is the perpendicular distance between congruent bases. The understanding includes rectangular, triangular, and other prisms whose base areas can be found from familiar formulas, including by decomposition, while excluding oblique prisms and more advanced generalized treatments.

Detailed Explanation: Calculate the volume of prisms

A prism has two matching, parallel bases. To find its volume, use

V=BhV=Bh

where:

  • BB is the area of one base
  • hh is the perpendicular distance between the two bases

The volume is measured in cubic units.

Example: Find the volume of a triangular prism with a triangular base that has a base of 66 cm and a height of 44 cm. The prism is 1010 cm long.

  1. Find the area of the triangular base.

    Use the triangle area formula:

B=12bhB=\frac{1}{2}bh

Substitute the measurements:

B=12(6)(4)=12 cm2B=\frac{1}{2}(6)(4)=12\text{ cm}^2
  1. Use the prism volume formula.

    The distance between the triangular bases is 1010 cm:

V=BhV=Bh V=(12)(10)=120 cm3V=(12)(10)=120\text{ cm}^3

Therefore, the volume of the triangular prism is

120 cm3\boxed{120\text{ cm}^3}

Remember to find the area of one base first, then multiply by the perpendicular distance between the bases.

Learn by doing: Calculate the volume of prisms

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Volume of a Rectangular Prism - Count Blocks


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