a sand pile in a shape of an upside-down cone has a volume of 350 m2 . The diameter of the base pof the pile is 7m. what is the height of the sand pile?
V = 1/3 pi r^2 h
350 = 1/3(pi) (3.5)^2 h
1050 = 12.25pi *h
1050 = 12.25(3.14) h
1050 = 38.465h
38.465h/38.465 = 1050/38.465
h = 27.29754
To find the height of the sand pile, we need to use the formula for the volume of a cone:
Volume = (1/3) * π * r^2 * h
Given:
Volume = 350 m^2
Diameter of the base = 7 m
To find the radius, divide the diameter by 2:
Radius = 7 m / 2 = 3.5 m
Now, we can plug in the values into the formula and solve for height:
350 = (1/3) * π * (3.5)^2 * h
First, calculate the value of (3.5)^2:
(3.5)^2 = 12.25
Now, rewrite the equation:
350 = (1/3) * π * 12.25 * h
To isolate the height (h), divide both sides of the equation by [(1/3) * π * 12.25]:
350 / [(1/3) * π * 12.25] = h
Calculate the value on the right-hand side of the equation:
[(1/3) * π * 12.25] = approximately 12.927
Divide 350 by 12.927 to find the height:
h ≈ 27.05 m
Therefore, the height of the sand pile is approximately 27.05 meters.