2 Calculus question that were on the final?

Question

I think I might have gotten these wrong. It's burning at the back of my mind on what the answers to these questions are. Can you please explain how to arrive at the solution?

1) The base of a triangle is slipping at a rate of 2cm/sec and the top is slipping at a rate of 3cm/sec. What is the rate when the base is 20cm and the height is 50cm? Is the area decreasing or increasing?


2) The volume of a topless can is 27pi. Find the radius and height. How do you know that these are the minimum dimensions?

*****The topless can is a cylinder******

Answer 1

1)

area of triangle, A = bh/2

differentiate with respect to time, t

dA/dt = b/2(dh/dt) + h/2(db/dt)

substitute b = 20, h = 50 , dh/dt = -3 and db/dt = -2
(negative sign indicates slipping)

dA/dt = 20/2(-3)+50/2(-2)

dA/dt = -30 - 50 = -80 cm^2/s.

since both base and height are slipping, area is decreasing

.

Answer 2

1. I don't understand what you mean by "slipping" so can,tbanswer this.

2. answer is r =3 and h =3. Minimum is always when h = r.