Question

How much concrete would you need for 35 caissons that are 4’ diameter and 40’ deep? Please answer in cubic yards. (A caisson is a deep pier of concrete that is poured in a hole that is drilled into the ground under where a building column will be place.)

Hint – volume of a cylinder = π * radius squared * height
Group of answer choices
35 caissons each at 502.4 cubic yards = 17,584 cubic yards
35 caissons each at 18.6 cubic yards = 651 cubic yards
35 caissons each at 5.93 cubic yards = 207.55 cubic yards

Answer 1

To calculate the amount of concrete needed for 35 caissons, each with a 4' diameter and 40' depth, you can use the formula for the volume of a cylinder:

Volume = π * r² * h

Where:

- π (pi) is approximately 3.14159

- r is the radius (half of the diameter)

- h is the height (depth)

First, find the volume of one caisson:

r = 4' / 2 = 2' (radius)

h = 40' (depth)

Volume of one caisson = π * (2')² * 40' = π * 4 * 40 = 160π cubic feet

Now, calculate the total volume of concrete needed for 35 caissons:

Total Volume = 35 * Volume of one caisson = 35 * 160π cubic feet

To convert cubic feet to cubic yards, you can use the fact that 1 cubic yard is equal to 27 cubic feet:

Total Volume in cubic yards = (35 * 160π cubic feet) / 27 cubic feet/cubic yard

Now, calculate this value:

Total Volume ≈ (35 * 160π) / 27 ≈ 5,932.67 cubic yards

So, you would need approximately 5,932.67 cubic yards of concrete for 35 caissons. However, none of the provided answer choices match this result exactly. The closest choice is:

35 caissons each at 5.93 cubic yards = 207.55 cubic yards

But it seems there might be a discrepancy in the calculation. The accurate result is approximately 5,932.67 cubic yards, not 207.55 cubic yards.

Step-by-step explanation:

if you need a personal homework helper dm me on ig, savant.carlos