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How many cubic yards of dirt must be dug to make a well with a diameter of 4 feet 6 inches and a depth of 42 feet?

Answer :

Final answer:

The well will contain approximately 11.8 cubic yards of dirt.

The volume was calculated using the formula for the volume of a cylinder and then converted from cubic feet to cubic yards.

Explanation:

To solve this problem, we first need to find the volume of the well. We know that the formula for the volume of a cylinder is πr2h, where r is the radius and h is the height.

In this case, the diameter of the well is given as 4 feet 6 inches, which is equivalent to 4.5 feet. Therefore, the radius would be half of the diameter, which is 2.25 feet.

The depth of the well is given as 42 feet, which will serve as our height (h) in the formula.

So by substituting the values into the formula, we get:

V = π(2.25)2*42 cubic feet, which simplifies to approximately 318.47 cubic feet.

One cubic yard is equivalent to 27 cubic feet. Therefore to convert the volume from cubic feet to cubic yards, we divide 318.47 cubic feet by 27.

So the well will contain approximately 11.8 cubic yards of dirt.

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