Question

please help!!! A high-altitude spherical weather balloon expands as it rises due to the drop in atmospheric pressure. Suppose that the radius r increases at the rate of 0.02 inches per second and that r = 36 inches at time t = 0. Determine the equation that models the volume V of the balloon at time t and find the volume when t = 360 seconds.

a. V(t) = 4π(0.02t)2; 651.44 in.3

b. V(t) = 4π(36 + 0.02t)2; 1,694,397.14 in.3

c. V(t) =4pi(0.02t)^3/3 ; 4690.37 in.3

d. V(t) = 4pi(36+0.02t)^3/3; 337,706.83 in.3

Answer 1

given:
\(\Large{dr\over dt}=0.02\\r(t=0)=36\)
Find V(t)
for sphere:
\(V = {4\over3}\pi r^3\)

Answer 2

differentiate V with respect to "t"

Answer 3

would it be answer b @electrokid ?

Answer 4

did you differentiate?

Answer 5

I believe so

Answer 6

ok, lets see it

Answer 7

I am sorry I meant choice d but I think I am doing it wrong, can you plaease explain it more @electrokid

Answer 8

yes. enter the derivative that you got here using the equation button.

Answer 9

\[V=\frac{ 4 }{ 3 }\pi(r+\Delta rt)^{3}\]

Answer 10

@electrokid

Answer 11

no.

Answer 12

well, i may have confused you.
It is a little bit easier than that

Answer 13

what is r(t) = radius as a function of time?
\[r(t)=\int dr=\int(0.02)dt=0.02t+C\]
we know that when t=0, r=36\[36=0+C\]
so, we have \[r(t)=0.02t+36\]

Answer 14

Okay what is the next step?

Answer 15

now,
\[V(t)={4\over3}\pi r^3(t)\\
\boxed{V(t)={4\over3}\pi(0.02t+36)^3}\]

Answer 16

so is the answer D?

Answer 17

D and B have the same functoin for V(t)
did you plug-in the value of "t" and find "V"?

Answer 18

yeah is it 1928838.459728091213476?

Answer 19

good. then thats your answer.

Answer 20

I did not calculate. plug in "t=360" in the function V(t)

Answer 21

so 1928838.459728091213476(360)? or \[\frac{ 4 }{ 3 }\Pi(0.02(360)+36)^3\]?

Answer 22

yep

Answer 23

which one?

Answer 24

I do not know. solve it. :)

Answer 25

well the answers I got do not match wat the answer should be...

Answer 26

694381845.5 and 3333032.9

Answer 27

nope. it comes out as 3.3771*10^5

Answer 28

Oh okay how did you get that?

Answer 29

What did I do wrong?

Answer 30

putting the numbers in the calculator, i guess!!

Answer 31

\[
{4\over3}\pi[0.02(360)+36]^3
\]

Answer 32

Ohhhh okay lol Thank you so much for all of your help!

Answer 33

yw.