Science:Math Exam Resources/Courses/MATH100/December 2015/Question 08 (b)/Solution 1
Let be the radius of the circle at the top of the water and be the height of the water.
Then, using the picture in part (a) with property of similar triangles give the ratio between and as
On the other hand, by the volume formula of cone, the volume of water can be written as
Therefore, by differentiating with respect to on both side, we obtain
Since the volume changes at the rate of , the rate of change of the height of the water at the height 10m is