Question

I need help with this

Answer 1

Answer:

  144 ft³

Step-by-step explanation:

This "irregular shape" is a composite shape that can be considered to be any of these compositions:

1. 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.
2. 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.
3. 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.

1.

  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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2.

  V = (4 ft)(3 ft)(6 ft) +(2 ft)(6 ft)(6 ft) = 72 ft³ +72 ft³ = 144 ft³

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3.

  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.