Question

Sand is poured at the rate of 10 m cube /min so as to form a conical pile whose altitude is always equal to the radius of its base

a) How fast is the radius increasing when it is 5 meters?
b) Find the rate at which the area of its base is increasing when the radius is 5m

Answer 1

So in V = (1/3)π r^2 h, the value of h = r, so we get
V = (1/3)π r^3

dV/dt = π r^2 dr/dt

a) plug in dV/dt = 10 m^3 and r = 5m, then solve for dr/dt

b) Area of base = πr^2
dA/dt = 2πr dr/dt
you have dr/dt from a) and r = 5

Answer 2

so sir reiny the answer i got in your solution is
a.0.4 m/min
b.4 m/min
that is right?

Answer 3

no ....

dV/dt = π r^2 dr/dt
10 = π(25)dr/dt
dr/dt = 10/(25π) = .127...

which of course means your second answer is also incorrect
dA/dt = 2πr dr/dt
= 2π(5)(.127...) = 4

You also had 4, but should not have obtained that answer if you used
the wrong answer to a)

very strange