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Sand is pouring from a pipe at the rate of 12 cm3/s. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?
Asked by Deepika Last Modified
Answer 
Harshit Bhardwaj
The volume of a cone (V) with radius (r) and height (h) is given by,
It is given that,
The rate of change of volume with respect to time (t) is given by,
[By chain rule]
It is also given that
.
Therefore, when h = 4 cm, we have:
Hence, when the height of the sand cone is 4 cm, its height is increasing at the rate of
.
Related Questions
The rate of change of the area of a circle with respect to its radius r at r = 6 cm is
(A) 10π (B) 12π (C) 8π (D) 11π
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