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Calculate the volume of prisms and cylinders

Volume of a prism or cylinder is understood as the amount of three-dimensional space occupied, found by multiplying the area of the uniform base by the perpendicular height: V=BhV=Bh, including V=πr2hV=\pi r^{2}h for a cylinder. Learners interpret and substitute measurements from diagrams or real contexts, distinguish radius from diameter, report cubic units, and select appropriate approximations for π\pi; more advanced treatments of oblique or irregular solids are not included.

Detailed Explanation: Calculate the volume of prisms and cylinders

Volume measures the space inside a three-dimensional object. For any prism or cylinder,

V=BhV=Bh

where:

  • BB is the area of the uniform base
  • hh is the perpendicular height of the solid

For a cylinder, the base is a circle, so B=πr2B=\pi r^2. Therefore,

V=πr2hV=\pi r^2h

Remember that the radius rr is half the diameter.

Example: Find the volume of a cylinder with diameter 10 cm10\text{ cm} and height 12 cm12\text{ cm}. Use π≈3.14\pi\approx 3.14.

  1. Find the radius.

r=102=5 cmr=\frac{10}{2}=5\text{ cm}

  1. Find the area of the circular base.

B=πr2B=\pi r^2 B≈3.14(5)2=3.14(25)=78.5 cm2B\approx 3.14(5)^2=3.14(25)=78.5\text{ cm}^2

  1. Multiply the base area by the perpendicular height.

V=BhV=Bh V≈78.5(12)=942 cm3V\approx 78.5(12)=942\text{ cm}^3

The volume of the cylinder is

942 cm3\boxed{942\text{ cm}^3}

For a prism, first find the area of its base—such as length ×\times width for a rectangular prism—and then multiply by the prism’s perpendicular height. Always report volume in cubic units.

Learn by doing: Calculate the volume of prisms and cylinders

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