The rate of leakage of water i.e rate of change of volume .

Height of the tank , base radius of the tank , base diameter .

To find the rate of change of radius at a height, we should know the radius of the base at that height.

If you take the cross section through vertex and the center of the base, you\\'ll have an isosceles triangle.

Now draw a line parallel to the base of this triangle at a height 14ft, then you\\'ll get two similar triangles.

one is bigger and the other one is smaller.

So, we have the relation

Where base and height of bigger triangle, base and height of smaller triangle.

Here .

.

Radius of the base at a height 14ft is .

To find the rate of change of radius we have to use the relation rate of change of volume.

Volume of the cone is ; r is radius of the base, h is height of the cone.

Now rate of change of volume with respect to time is

At height 14ft and base radius 2.15ft

               ()

.

The rate of change radius of the water level is .