Question

A snowball is melting in the sun. It is noted that its surface decreases at a rate of 3cm2/s at the moment when its diameter is 8/picm. The goal here is to determine the rate at which the diameter varies at that same moment.

To solve this problem, let x be the diameter of the snowball in cm, A its area in cm2, and t the time in seconds (s).

(a) Express A as a function of x.

A= __________ cm2

(b) What is the value of dA over dx when x=8/pi? Give the exact value.

dA over dx= __________ cm

(c) Using our previous results, give the (exact) value of dx over dt when x=8/pi cm.

Answer 1

seems like we want to use the formula for the surface area of a sphere.

Answer 2

well i need help ASAP pls

Answer 3

that is the help .... what is the formula for the surface area of a sphere?

Answer 4

i can find part A
but i am stuck on part B

Answer 5

we take an implicit derivative of the Area formula

Answer 6

what did you get for part a?

Answer 7

part b is dA/dx

Answer 8

4pi(x/2)^2
for part a

Answer 9

4 pi r^2

but r = d/2

4 pi (d/2)^2

simplify

4 pi d^2/4 = pi d^2

but they want x instead of d ... like a name matters sooo

A = pi x^2

Answer 10

is that the answer for A ^ ?

Answer 11

i hope so, otherwise im just doing my taxes :)

Answer 12

ok so whats the part B then ? C:

Answer 13

part B is to find the derivative wrt.x of course ...

dA/dx = ?

Answer 14

pls give me the answer i am confused T_T

Answer 15

idont just give out answers, that is NOT what this site is used for.

Answer 16

ok if i post my work here can you help me identify the error ?

Answer 17

ye si can

Answer 18

ok i will post my solution 1 min pls

Answer 19

(b) is asking for dA/dx

so dA/dx = dA/dt * dt/dx

that's all i know. am i on the right path ?

Answer 20

dA/dx is just a 'normal' derivative. in this case its a simple power rule.

given A = pi x^2, just read this as if its was something like: y = 3x^2

Answer 21

what do you mean by normal derivative ? am i just suppose to plug 8/pi in A=pi x^2 to find the answer for B ?

Answer 22

What is the value of dA/dx when x=8π?

well, what is the derivative of A = pi x^2?

derive, and then plug in x=8pi

Answer 23

we have a constant and x to a power ... use the power rule

Answer 24

so the derivative is pi*2x

Answer 25

refrech with f5 to clear up the odd marks

Answer 26

yes, the derivative of A = pi x^2 is A' = 2pi x

Answer 27

your post says x=8pi (not x=8/pi) ... so if that is an error, then use what your problem wants you to use.

Answer 28

yes i just copied the question so it is not showing the divide sign

Answer 29

but yes, IF x=8/pi the dA/dx = 16

Answer 30

and part C you alluded to earlier, the chain rule :\[\frac{dA}{dt}=\frac{dA}{dx}\frac{dx}{dt}\]

Answer 31

ok i just fixed my question up
i hope that clarifies things up

Answer 32

oh it does :)

Answer 33

so everything we were doing so far is correct ?

Answer 34

yes, everything so far has been fine

Answer 35

and since we know dA/dt from the infomation, and dA/dx from part B, the rest is just simple division

Answer 36

ok so i understand part a and b now but i am still confused on part C

Answer 37

\[\frac{dA}{dt}=\frac{dA}{dx}\frac{dx}{dt}\]
we know everything but dx/dt ...

Answer 38

ohhhhh ok so it's -3 / 16 ?

Answer 39

yes :)

Answer 40

alright thanks for the help. i will try to enter these answers and if they are wrong i will be back again for more help c: