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.
Worked example: a cylindrical tank
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.
A general problem-solving approach
Identify the shape: is it a prism (flat, matching ends) or a cylinder (circular ends)?
Write down what you know: base dimensions or radius, and height.
Check the units — the answer is always in cubic units.
Comparing volumes
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.