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?
To find the height of the sand pile, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h,
where V is the volume, π (pi) is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cone.
Given that the volume of the sand pile is 350 m^3 and the diameter of the base is 7 m, we can calculate the radius (r) by dividing the diameter by 2:
r = 7m / 2 = 3.5m.
Now, we can substitute the known values into the volume formula:
350 m^3 = (1/3) * π * (3.5m)^2 * h.
Simplifying the equation, we get:
350 m^3 = (1/3) * π * 12.25m^2 * h.
Since we know that the volume is 350 m^3, we can rearrange the equation to solve for the height (h):
h = (350 m^3) / [(1/3) * π * 12.25m^2 ].
By evaluating the expression on the right-hand side, using the value of π (pi) approximately equal to 3.14159, we can find the height of the sand pile.