Problema Solution
Grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height. How high is the pile (to the nearest hundredth of a foot) when it contains 1050 ft3 of grain?
Answer provided by our tutors
let 'r' represent the radius of the pile, then its height is '(2r)/3'
volume of a cone:
V = (PI*r^2*h)/3, where 'PI' is the numeric constant approximated by 3.12, 'r' is the radius and 'h' is the height
1050 = (PI*r^2*(2r)/3)
solving for 'r' we have r=7.994
the radius is approximately 8 feet, the diameter 16 feet and the approximate height of the grain pile:
16/3 = 5 1/3
the grain pile is approximately 5 1/3 feet in height = 5.33 feet