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Word problems relating volume of prisms and cylinders

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Word Problems: Prisms and Cylinders

Volume word problems about prisms and cylinders ask you to identify the shape, pick base area times height for a prism or pi r squared h for a cylinder, and calculate with the given measurements. Worked through with a cylindrical tank example finding a capacity of about 62.8 cubic meters.

Applying the volume formulas

Word problems about prisms and cylinders ask you to recognize the shape, pick the right formula, and carry out the calculation with the given measurements. The two formulas to know are volume of a prism = base area × height and volume of a cylinder = πr²h.

A cylindrical tank word problem A cylindrical water tank with radius 2 meters and height 5 meters. Applying the cylinder volume formula, pi times radius squared times height, gives a capacity of about 62.8 cubic meters. r = 2 m h = 5 m Question: how much water can the tank hold? V = πr²h = π × 2² × 5 V ≈ 62.8 m³
A cylindrical tank with radius 2 m and height 5 m holds about 62.8 cubic meters.

Since the tank is a cylinder, use V = πr²h. Squaring the radius gives 2² = 4, multiplying by π gives about 12.57, and multiplying by the height of 5 gives a capacity of about 62.8 cubic meters.

  1. Identify the shape: is it a prism (flat, matching ends) or a cylinder (circular ends)?
  2. Write down what you know: base dimensions or radius, and height.
  3. Apply the matching formula from volume of a prism or volume of a cylinder.
  4. Check the units — the answer is always in cubic units.

Some problems ask you to compare a prism's capacity to a cylinder's, such as which container holds more. Calculate each volume separately using its own formula, then compare the results directly since both answers are already in the same cubic units.

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