How many cubic yards of concrete will it take to fill a cylindrical column that is 16 feet high and whose diameter is 4 feet?
Use pi=3.14
(round your answer to the nearest TENTH)
If a cubic yard of concrete costs $75, using the rounded answer from above, what would be the cost for the concrete (rounded to the nearest dollar)
The volume is pi D^2/4 * H
In cubic ft, this is
(3.14)*(1/4)*(4)^2*(16)= 201.0 ft^3. Divide by 27 ft^3/yard^3 for the number of cubic yards.
Then multipy by $75/yard^3 for the cost.
would it be 7.4 cubic yards
and 558 dollars
Yes.
To find the volume of a cylindrical column, we need to use the formula V = πr^2h, where V is the volume, π is a constant (approximately 3.14), r is the radius, and h is the height.
First, we need to find the radius. The diameter (d) of the column is given as 4 feet. The radius (r) is half the diameter, so r = d/2 = 4/2 = 2 feet.
Next, we can substitute the values of π, r, and h into the formula to calculate the volume (V).
V = πr^2h = 3.14 * (2^2) * 16 = 3.14 * 4 * 16 = 200.96 cubic feet.
To convert cubic feet to cubic yards, we need to divide the volume by 27 (1 cubic yard = 27 cubic feet).
200.96 cubic feet ÷ 27 = 7.44 cubic yards.
Rounding to the nearest tenth, the answer is approximately 7.4 cubic yards of concrete.
To find the cost for the concrete, we multiply the volume (7.4 cubic yards) by the cost per cubic yard ($75).
Cost = volume * cost per cubic yard = 7.4 * 75 = 555.
Rounding to the nearest dollar, the cost for the concrete would be approximately $555.