Question

1. The area A = πr2 of a circular oil spill changes with the radius. At what rate does the area change with respect to the radius when r = 3ft?
6π ft2/ft
3π ft2/ft
6 ft2/ft
9π ft2/ft
2. The height of a cylinder with a fixed radius of 6 cm is increasing at the rate of 3 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is 20cm.
36π
108π
360π
None of these

Answer 1

Also these two!
1. A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by V = x2h cm3. Find the rate at which the volume of the box is changing when the edge length of the base is 10 cm, the edge length of the base is increasing at a rate of 3 cm/min, the height of the box is 5 cm, and the height is decreasing at a rate of 1 cm/min.
The volume of the box is decreasing at a rate of 200 cm3/min.
The volume of the box is increasing at a rate of 400 cm3/min.
The volume of the box is decreasing at a rate of 400 cm3/min.
The volume of the box is increasing at a rate of 200 cm3/min.
2. A 15-ft ladder rests against a vertical wall. If the top of the ladder slides down the wall at a rate of 0.33 ft/sec, how fast, in ft/sec, is the bottom of the ladder sliding away from the wall, at the instant when the bottom of the ladder is 9 ft from the wall? Answer with 2 decimal places. Type your answer in the space below. If your answer is a number less than 1, place a leading "0" before the decimal point (ex: 0.35).

Answer 2

so 1 would be 6π ft2/ft??

Answer 3

6pi

Answer 4

Lets see your work

Answer 5

\[A=pir^2\]
dA/dt=2pir
dA/dt=2(pi)(3)
6(pi)

Answer 6

My bad...for this first question you only needed to use the power rule and calculate dA/dr
...the derivative you calculated is dA/dr

Answer 7

on to the cylinder...first you need to look up the volume of a cylinder

Answer 8

i am so confused.can you show me steps of number 1?

Answer 9

sure...hang on

Answer 10

A = pi*r^2 agree

Answer 11

you there?

Answer 12

yes sorry

Answer 13

so by the power rule what is da/dr?

Answer 14

dA/dr...(capital A)

Answer 15

i dont know

Answer 16

are you taking calculus?

Answer 17

yes

Answer 18

ok. what does the power rule say?

Answer 19

i dont remebr

Answer 20

ok I need you to look it up and I will help you through these problems

Answer 21

if y = x^n
then dy/dx =?

Answer 22

i understand this problem. i don't understand the cylinder and the rectangle

Answer 23

ok,,,,what is the equation for the volume of cylinder?

Answer 24

\[V=pir^2h\]

Answer 25

what is dV/dt assuming height is constant?

Answer 26

\[dV/dt=\pi2r*dr/dt\]

Answer 27

oops what happened to h?

Answer 28

dh/dt

Answer 29

no...h is constant

Answer 30

oh so it just stays h?

Answer 31

Yes...because in this particular problem it is constant so you would treat it just like pi...

Answer 32

ok

Answer 33

remember the if y = constant*x^n then
dy/dx = constant*nx^(n-1)

Answer 34

So what is dV/dt...

Answer 35

what does dr/dt equal?

Answer 36

r is 6 but what is dr/dt?

Answer 37

fixed radius of 6 cm is increasing at the rate of 3 cm/min.

Answer 38

so dr/dt = ....

Answer 39

is increasing at the rate of 3 cm/min.

Answer 40

oh i forgot that part so dr/dt=3?

Answer 41

yes...3 cm/mim

Answer 42

so lets see your expression for dV/dt

Answer 43

so it should equal 720 pi?

Answer 44

I want ot make sure you have dV/dt correct then we substitute

Answer 45

dV/dt=pi*h*2r*dr/dt

Answer 46

great!!! now substitute and put in your units where applicable

Answer 47

dV/dt=(20)*(pi)*(2*6)*(3)

Answer 48

I would suggest you put in your units but that is up to you...

Answer 49

so answer is 720pi?

Answer 50

numerically ..yes it is 720 pi...but there are units with that answer which can help you understand these rate problems

Answer 51

I will be back on later tonight...see what you can do with the next two problems.

Answer 52

i only need help with the rectangular box. can we do it real quick?

Answer 53

Hint: V=x^2*h but both x and h are changing as a function of time.
So how do you calculate dV/dt...you will need to use the product rule of differentiation

Answer 54

Thank you i need to go to dinner. will try after dinner

Answer 55

your welcome