You are watching: If a snowball melts so that its surface area decreases at a rate of 1 cm^2/min find the rate
My answer is wrong. Can some one aid me solve?
Given: The rate of decrease of the surchallenge location is $3~frac extcm^2 extmin$. I f we let $t$ be time in (in minutes) and also $s$ be the surchallenge area (in cm$^2$), then we are offered that $fracdsdt = -3~ extcm^3$
Unknown: The price of decrease of the diameter as soon as the diameter is $8$ cm
If we let $x$ be the diameter, then we desire to uncover $fracdxdt$ once $x = 8$ cm. If the radius is $r$ and the diameter is $x = 2r$ then $r = frac12x$ and also $S = 4pi r^2$, $x=2r$, then $r=frac12x$$S=pi x^2 =-frac32pi 8$
My answer is wrong. Can some one assist me understand?
edited Mar 16 "15 at 11:51
N. F. Taussig
60.8k1212 gold badges4848 silver badges6666 bronze badges
asked Mar 16 "15 at 11:14
2,8821010 gold badges4242 silver badges7474 bronze badges
Add a comment |
2 Answers 2
Active Oldest Votes
We have actually that the surconfront location formula is:
$$SA = 4pi r^2$$
If we take the derivative via respect with time, we get:
$$fracdSAdt = 8pi r fracdrdt$$
Now, from the difficulty we are offered that $fracdSAdt = -3$, and $r = 4$
Now we have the right to find $fracdrdt$:
$$ 32pi fracdrdt = -3, fracdrdt = -frac332pi$$
Now, we deserve to also make the relation that:
$$d = 2r, fracdddt = 2fracdrdt = 2*left(-frac332pi ight) = -frac632pi$$
Thus our diameter decreases at a price of $frac632pi$
answered Mar 16 "15 at 11:22
Varun IyerVarun Iyer
5,8581313 silver badges2929 bronze badges
Add a comment |
Due to the fact that the question is asking around the diameter quite than the radius, you have the right to likewise deal straight via the diameter from the start and conserve some job-related later. This is based on the reality that $r=fracd2$ (radius is constantly half the diameter).
$$SA=4 pi r^2$$$$SA=4 pi igg( fracd2 igg)^2$$$$SA=4 pi igg( fracd^24 igg)$$$$SA=pi d^2$$
Now you have the right to take the derivative with respect to time.
$$fracdSAdt=2 pi d fracdddt$$
Now just plug in the provided indevelopment and also fix for $fracdddt$.
$$-3=2 pi (8) cdot fracdddt$$$$frac-316 pi=fracdddt$$
So the diameter is decreasing at a price of $frac316 pi$.
Here"s a great webwebsite that describes this problem in a little bit even more information. The numbers are different, however the procedure is similar.
edited Jan 30 "19 at 6:35
answered Jan 8 "19 at 15:02
Jake OJake O
17655 bronze badges
Add a comment |
Thanks for contributing a solution to rwandachamber.orgematics Stack Exchange!Please be sure to answer the question. Provide details and share your research!
But avoid …Asking for help, clarification, or responding to other answers.Making statements based on opinion; ago them up through references or individual endure.
Use rwandachamber.orgJax to format equations. rwandachamber.orgJax recommendation.
To learn more, view our tips on creating great answers.
Sign up or log in
Sign up using Google
Sign up using Facebook
Sign up using Email and also Password
Post as a guest
Email Required, yet never shown
Blog post as a guest
Required, but never before shown
Article Your Answer Discard
Not the answer you're looking for? Browse other inquiries tagged calculus or ask your very own question.
Featured on Meta
associated price difficulty of a spright here.
See more: Wasteland Flora Overhaul (Dead) V2.8A, New Play Through Mod Suggestions
Rate vs radius?
implicit differentiation with associated prices
Related prices via snowround
Related Rate Question: Water is leaking out of an inverted conical tank at a rate of 9,500 cm3/min
Related Rates- Snowsphere Melting...
Related prices - Melting snowsphere
connected price trouble of a spright here.
Calculus associated prices snowsphere radius trouble
Hot Netjob-related Questions even more hot concerns
Subscribe to RSS
Question feed To subscribe to this RSS feed, copy and paste this URL right into your RSS reader.
Stack Exchange Network-related
website style / logo © 2021 Stack Exreadjust Inc; user contributions licensed under cc by-sa. rev2021.9.13.40199