Name: Brandon
Who is asking: Student
Level of the question: Secondary

Question: This one HW problem is just devastating. I think there is a typo, and I'll show you where, but I'm unsure of part of the work too.

An Oil Tanker Spills 100,000 cubic meters of oil, which forms a slick that spreads on the water surface in a shape best modeled by a circular disc is increasing at a rate of 3m/min (it doesn't state what is increasing at 3m/min, so I'm assuming Radius until I can ask my teacher.) At t=T, the area of the "circular" slick reaches 100pi Sq. meters.

A) how fast is the area of the slick increasing at t=T
B)How fast is the thickness of the slick decreasing at t=T
C)Find the rate of change of the area of the slick with respect to the thickness at t=T.

I've got:
volume= 100,000 m3
Radius @ t=T is 10
since radius is 10 @ t=T, then height(depth) must be 318.31 m

but i can't figure out how to find the change in height.

Also is question A simply the constant 3m/min?

Thanks a ton!



The volume of oil in the circular disk is given by

V = r2 h

where r is the radius of the disk and h is its thickness. In your situation V is a constant, 100,000 m3, and both r and h change with time. I want to emphasize the fact that r and h vary with time by writing r = r(t) and h = h(t). Hence you have

100,000 = r(t)2 h(t)

If you now differentiate both sides with respect to t you will have 0 on the left side and the right side will be an expression in r(t), h(t), r'(t) and h'(t).

Does this help?