Question

an excavation for a building foundation is 60.0 feet long, 35.0 feet wide, and 14.0 feet deep. how many cubic yards of soll are removed? round the answer to 3 significant digits. 29,400 cu ft 29,400 cu ft 29,400 ft 29,400 sq ft

Explanation:

Step1: Calculate the volume in cubic feet

The volume \( V \) of a rectangular prism (which the excavation resembles) is given by the formula \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height (depth here).
Given \( l = 60.0 \) ft, \( w = 35.0 \) ft, \( h = 14.0 \) ft.

$$ V = 60.0 \times 35.0 \times 14.0 $$

$$ V = 60.0 \times 490.0 = 29400 \text{ cubic feet} $$

Step2: Convert cubic feet to cubic yards

We know that \( 1 \) yard \( = 3 \) feet, so \( 1 \) cubic yard \( = 3^3 = 27 \) cubic feet.
To convert cubic feet to cubic yards, divide the volume in cubic feet by \( 27 \).

$$ \text{Volume in cubic yards} = \frac{29400}{27} \approx 1088.89 $$

Wait, but the options provided seem to be about the cubic feet volume (maybe a typo in the question's final ask, or the options are for the cubic feet step). Let's recheck: the question says "How many cubic yards...", but the options are all 29400 with different units (cu ft, cu ft, ft, sq ft). Assuming the question might have a mix-up, but first, the volume in cubic feet is \( 60 \times 35 \times 14 = 29400 \) cu ft. So the correct option for cubic feet (if that's the intended answer here) is the one with "cu ft" (cubic feet).

Answer:

29400 cu ft (the option with "29400 cu ft" as the volume in cubic feet, before converting to cubic yards; if the question intended cubic feet, this is the answer. If cubic yards was intended, the calculation above shows ~1089 cu yd, but the options don't match, so likely the question's final ask has a mix-up, and the cubic feet volume is 29400 cu ft.)