An illustration shows an inverted U-shaped structure made up of three rectangular prisms. Two identical rectangular prisms are placed on either side of a center rectangular prism. The side prisms are 16 inches long, 7 inches wide, and 7 inches high. The prism placed in between the two rectangles is 8 inches wide and 10 inches long.
What is the volume of the composite figure?
To find the volume of the composite figure, we first need to calculate the volume of each individual prism.
Volume of the side prisms:
Length = 16 inches
Width = 7 inches
Height = 7 inches
Volume = Length x Width x Height
Volume = 16 x 7 x 7
Volume = 784 cubic inches
Since there are two identical side prisms, the total volume of both side prisms combined is:
Total volume of side prisms = 2 x 784
Total volume of side prisms = 1568 cubic inches
Volume of the center prism:
Length = 10 inches
Width = 8 inches
Height = 7 inches
Volume = Length x Width x Height
Volume = 10 x 8 x 7
Volume = 560 cubic inches
Now, to find the total volume of the composite figure, we add the volumes of the side prisms and the center prism:
Total volume = Total volume of side prisms + Volume of center prism
Total volume = 1568 + 560
Total volume = 2128 cubic inches
Therefore, the volume of the composite figure made up of three rectangular prisms is 2128 cubic inches.