With some volume word problems you can use the four step process model to create and implement a plan to solve the volume problem.

The figure below summarizes the four-step problem-solving process.

Practice using the four step problem solving process.

Pause and Reflect

If the base of a rectangular prism were a rectangle that was not a square, how could you determine the area of the base?

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Check Your Answer

A square is a special type of rectangle, so if the base is a rectangle that is not a square, you can still use the area formula for a rectangle. The difference would be that the base and height of the rectangle would not be the same.

Suppose a right rectangular prism has a base area of 50 square yards and a volume of 325 cubic yards. How could you determine the height of the prism?

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Check Your Answer

Write an equation using the volume formula for a prism, V = Bh. You know the area of the base, B = 50 square yards and the volume of the prism, V = 325 cubic yards. Substitute these values into the volume formula to generate the equation, 325 = 50h and solve for h.
325 over 50 325 50 = 50h over 50 50h 50
6.5 = h

Practice

Source: Djenne2, Olivierkeitha, Wikimedia Commons

1. A traditional house in Djenne, Mali, is built from a mixture of earth and cement in the shape of a rectangular prism. If a house has a length of 461 over 2 1 2 feet, a width of 30 feet, and is 10 feet tall, what is the interior volume of the house?

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   Need a hint?

   Use the reference materials to determine the volume formula for a prism as well as any area formulas you may need. Remember the height of a prism is different from the height of the base.
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   Check Your Answer

   Since the figure is a rectangular prism, use the volume formula for a prism, V = Bh, and the area formula for a rectangle, A = bh.
   Area of the base:
   A = bh = (461 over 2 1 2 feet)(30 feet) = 1,395 square feet
   
   Volume of the prism:
   V = Bh = (1,395 square feet)(10 feet) = 13,950 cubic feet
   
   The volume of the house is 13,950 cubic feet.
2. In Mexico City, townhouses are built in the shape of rectangular prisms adjacent to each other. The figure below shows three such townhouses with the same depth, 15.5 meters.
   

   Source: Mexican Architecture, Joaquín Martínez Rosado, Wikimedia Commons

   Write an equation that you could use to determine the volume of each of the three townhouses.

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   Need a hint?

   Use the volume formula for a prism and the area formula for the shape of the base of the prism. Use the reference materials to help you identify the volume and area formulas if necessary.
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   Check Your Answer

   Volume of green townhouse
   B = bh = (12.5 m)(15.5 m)
   V = Bh = (12.5 m)(15.5 m)(21 m)
   
   Volume of blue townhouse
   B = bh = (10 m)(15.5 m)
   V = Bh = (10 m)(15.5 m)(25 m)
   
   Volume of pink townhouse
   B = bh = (15.5 m)(15.5 m)
   V = Bh = (15.5 m)(15.5 m)(17 m)
3. Which townhouse has the greatest volume?

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   Need a hint?

   Use your equation from Question 2. Calculate the volume of each townhouse, and then compare the decimal numbers.
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   Check Your Answer

   Volume of green townhouse = (12.5 m)(15.5 m)(21 m) = 4,068.75 m³
   Volume of blue townhouse = (10 m)(15.5 m)(25 m) = 3,875 m³
   Volume of pink townhouse = (15.5 m)(15.5 m)(17 m) = 4,084.25 m³
   
   The pink townhouse has the greatest volume.