Question

a machine 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, what is the height of the pile? Please include steps. Thanks!

Answer 1

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 $V = \frac{1}{3} \pi r^{2} h$

⇒ $100 = \frac{1}{3} \times (\frac{22}{7}) \times (\frac{h}{4} )^{2} \times h$ {From equation (1)}

⇒ $h^{3} = 1527.27$

⇒ h = 11.52 meters. (Answer)