Amachine starts dumping sand at the rate 20 m^3/min, forming a pile in the shape of a cone. the height of the pile is always twice the length of the base diameter. after 5 minutes, how fast is the base radius increasing? include steps.

Base radius is increasing by 2.88 m after 5 minutes

Step-by-step explanation:

Given:-

Height of cone (h) =2 base diameter(d)

Machine starts dumping sand at the rate of 20

So,

Volume of cone in 1 min = 20

Now, Volume of cone in 5 mins = Volume of cone in 1 min

Volume of cone in 5 mins = 20

Volume of cone in 5 mins = 100 ---------(equation 1)

Now, Let base diameter of cone = b

height of the cone = h

formula for volume of cone is,

Volume of cone (V) =

----(since r=)

 ---------(equation 2)

Now substituting equation 1 in equation 2,

---------(as )

By cube rooting both the sides we get,

----------------(diameter)

 ---------------(radius of base at 5 mins)

Therefore base radius is increasing by 2.88 m after 5 minutes

mean= 4.68

variance= 1.0296

Step-by-step explanation:

mean= n×p

n=6

p=0.78

mean= 6×(0.78)

           = 4.68

variance= n×p×(1-p)

             = 6 × 0.78×(1-0.78)

              = 1.0296