Answer:
(c) 115.2 ft³
Step-by-step explanation:
The volume of a composite figure can be found by decomposing it into figures whose volumes are easy to compute. Here, the figure can be nicely represented as a cube and a square pyramid.
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Cube
The volume of the cube on the left is given by ...
V = s³
V = (4.2 ft)³ = 74.088 ft³
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Pyramid
The volume of the pyramid on the right is given by ...
V = 1/3Bh . . . . . where B is the area of the square base
V = 1/3(s²)h = (4.2 ft)²(7 ft) = 41.16 ft³
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Total
The volume of the composite figure is the sum of these volumes:
cube volume + pyramid volume = 74.088 ft³ +41.16 ft³ = 115.248 ft³
The volume of the composite figure is about 115.2 ft³.
