Answer:
11.52 meters.
Step-by-step explanation:
At the rate of 20 m^3/min, a machine is dumping sand, forming a pile of the shape of a cone.
Therefore, in 5 minutes it will dump (20 × 5) = 100 m³.
Now, the length of the base diameter is always half of the height of the pile.
Let the height after 5 minutes is h meters.
So, h = 2(2r) = 4r {Where, r is the radius of the cone after 5 minutes} ........ (1)
Now, volume of a cone is given by [tex]V = \frac{1}{3} \pi r^{2} h[/tex]
⇒ [tex]100 = \frac{1}{3} \times (\frac{22}{7}) \times (\frac{h}{4} )^{2} \times h[/tex] {From equation (1)}
⇒ [tex]h^{3} = 1527.27[/tex]
⇒ h = 11.52 meters. (Answer)
