Question

sand is falling into a cone whose height is always 4 times the diameter. if the sand is falling at a rate of 500 cubic meters per hours how fast is the radius increasing when the volume is 1000pi/3 cubic meters

Answer 1

Let r = radius , V = volume, h = height
h = 8r
V =1/12( pi.r^2.h)
V = 1/12(pi.r^2.8r)
V= 2/3(pi.r^3)
dv/dr = 4/3.pi.r^2
it is given that dv/dr is 1000pi/3
1000pi/3 =4/3.pi.r^2
1000 = 4r^2
r = square root of 250 meters
the radius is increasing at a rate of square root of 250 meters per hour