Answer:
Volume(V) of a circular cone is given by :
......[1] where r is the radius and h is height of the cone respectively.
Given: Radius of cone(r) = 16 cm and height of cone(h) = 8 cm
or
r =2h
Substitute in [1]; we have
......[2]
It is also, given the rate i.e,
Differentiate V with respect to t in equation [2] we get;
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To find the rate of depth of the water when tank is 6 cm deep.
Simplify:
Substitute h = 6 cm we have;
or
[Use ]
Simplify:
Therefore, the rate of depth of the water changing is,