### Math Notes

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#### Solid Geometry Solutions

##### Topics || Problems

A trench is 180 ft. long and 12 ft. deep, 7 ft. wide at the top and 4ft. at the bottom. How many cubic yards of earth have been removed?

$$Vol = A_{trapezoid} ~(180)$$

$$A_{trapezoid} = \frac{7+4}{2} (12)$$

$$A_{trapezoid} =66$$

$$Vol = 66 (180)$$

$$Vol =11880~ft^3$$

$$3~ft = 1~yd$$

$$Vol = 11880 \frac{1yd^3}{27ft^3}$$

$$Vol = 440 ~yd^3$$ Answer