SOLVING VOLUME PROBLEMS

When we solve a real-world problem involving the volume of a prism, we can choose to use either of the volume formulas we know.

Example 1 :

A terrarium is shaped like a rectangular prism. The prism is 25 inches long, 13 inches wide, and 16 inches deep. What is the volume of the terrarium ?

Solution :

Step 1 :

From the given information, we can have the following figure. 

Step 2 : 

In the above figure, the base is in the shape of a rectangle with length 25 inches and width 13 inches.  

Therefore, 

Area of the base  =  length x width 

Area of the base  =  25 x 13

Area of the base  =  325 square inches.

Step 3 : 

Volume of the terrarium  =  Volume of rectangular prism 

Volume of the terrarium  =  Base area x Height 

Volume of the terrarium  =  325 x 16

Volume of the terrarium  =  5200 cubic inches

Example 2 :

A rectangular swimming pool is 15 meters long, 10 1/2 meters wide, and 2 1/2 meters deep. What is its volume?

Solution :

Step 1 :

From the given information, we can have the following figure. 

Step 2 : 

In the above figure, the base is in the shape of a rectangle with length 15 meters and width 10 1/2 meters. 

Therefore, 

Area of the base  =  length x width 

Area of the base  =  15 x 10 1/2

Area of the base  =  15 x 10.5

Area of the base  =  157.5

Area of the base  =  157.5 square inches.

Step 3 : 

Volume of swimming pool  =  Volume of rectangular prism 

Volume of the swimming pool  =  Base area x Height 

Volume of the swimming pool  =  157.5 x 2 1/2

Volume of the swimming pool  =  157.5 x 2.5

Volume of the swimming pool  =  393.75

Volume of the swimming pool  =  393 75/100

Volume of the swimming pool  =  393 3/4 cubic meters

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