VOLUME OF COMPOSITE SOLIDS

Example 1 : 

Allie has two aquariums connected by a small square prism. Find the volume of the double aquarium.

Solution :

Step 1 :

Find the volume of each of the larger aquariums.

Volume  =  Base area x Height

Volume  =  (4 x 3) x 3

Volume  =  12 x 3

Volume  =  36 cubic ft. 

Step 2 :

Find the volume of the connecting prism.

Volume  =  Base area x Height

Volume  =  (2 x 1) x 1

Volume  =  2 x 1

Volume  =  2 cubic ft.

Step 3 :

Add the volumes of the three parts of the aquarium.

V  =  36 + 36 + 2

V  =  74 cubic ft.

The volume of the aquarium is 74 cubic ft.

Example 2 : 

The figure is composed of a rectangular prism and a triangular prism. Find the volume of the figure.

Solution :

Step 1 :

Find the volume of each of the larger aquariums.

Volume  =  Base area x Height 

Volume  =  (30 x 13) x 13

Volume  =  5070 cubic in.

Step 2 :

Find the volume of the triangular prism.

Volume  =  (1/2) x Base area x Height 

Volume  =  (1/2) x (30 x 9) x 13

Volume  =  1755 cubic in.

Step 3 :

Add the volumes of the two parts of the aquarium.

V  =  5070 + 1755

V  =   6825 cubic in.

The volume of the given figure is 6825 cubic in.

Example 3 : 

The figure is composed of a rectangular prism and a triangular prism. Find the volume of the figure.

Solution :

Step 1 :

Find the volume of each of the larger aquariums.

Volume  =  Base area x Height 

Volume  =  (12 x 6) x 4

Volume  =  288 cubic ft.

Step 2 :

Find the volume of the triangular prism.

Volume  =  (1/2) x Base area x Height 

Volume  =  (1/2) x (6 x 6) x 4

Volume  =  72 cubic ft.

Step 3 :

Add the volumes of the two parts of the aquarium.

V  =  288 + 72

V  =   360 cubic ft.

The volume of the given figure is 360 cubic ft.

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