SOLUTION: Hi Stuck on this, can someone please help The total surface area S of a closed cone of base radius r cm and perpendicular height h cm is given byS = pir^2 + pi r sqrt(r^2 +

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi Stuck on this, can someone please help The total surface area S of a closed cone of base radius r cm and perpendicular height h cm is given byS = pir^2 + pi r sqrt(r^2 +      Log On


   

Question 383609: Hi
Stuck on this, can someone please help
The total surface area S of a closed cone of base radius r cm and perpendicular height h cm is given byS = pir^2 + pi r sqrt(r^2 + h^2). If r and h are each increasing at the rate of 0.25 cm s^-1, find the rate at which S is increasing at the instantwhen r = 3 and h = 4.
Thank You,
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
S+=+pi%2Ar%5E2+%2B+pi%2Ar%2Asqrt%28r%5E2+%2B+h%5E2%29
Differentiate with both r and h as variables.

Substitute r=3, h=4, dr=dh=0.25,

.
.
dS=%283%2F2%29%2Api%2Bpi%2A3%2A%281%2F%282%2A5%29%29%2A%283%2F2%2B2%29%2B+pi%2A%285%2F4%29
.
.
dS=pi%2A%28%283%2F2%29%2B%2821%2F20%29%2B%285%2F4%29%29
.
.
dS=pi%2A%28%2830%2F20%29%2B%2821%2F20%29%2B%2825%2F20%29%29
.
.
dS=%2819%2F5%29%2Apicm%5E2%2Fs