Answer:
144 ft³
Step-by-step explanation:
This "irregular shape" is a composite shape that can be considered to be any of these compositions:
- extending the middle horizontal surface cuts the shape into two blocks: upper left: 2 ft high, 3 ft wide, 6 ft deep; and lower: 2 ft high, 9 ft wide, and 6 ft deep.
- extending the middle vertical surface cuts the shape into two blocks: left: 4 ft high, 3 ft wide, and 6 ft deep; and right: 2 ft high, 6 ft wide, and 6 ft deep.
- A larger block with a smaller block cut out of the upper left: larger block: 4 ft high, 9 ft wide, and 6 ft deep; cutout: 2 ft high, 6 ft wide, and 6 ft deep.
The volume of any one of these blocks is the product of height, width, and depth. The above decompositions are evaluated here.
<h3>1.</h3>
V = HWD
V = (2 ft)(3 ft)(6 ft) +(2 ft)(9 ft)(6 ft) = 36 ft³ + 108 ft³ = 144 ft³
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<h3>2.</h3>
V = (4 ft)(3 ft)(6 ft) +(2 ft)(6 ft)(6 ft) = 72 ft³ +72 ft³ = 144 ft³
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<h3>3.</h3>
V = (4 ft)(9 ft)(6 ft) -(2 ft)(6 ft)(6 ft) = 216 ft³ -72 ft³ = 144 ft³
Travis must use 144 ft³ of concrete to make the block.
