Question

what is volume of sphere?
thank you

Answer 1

formula ?
\(\Large V_{sphere}= (4/3)\pi r^3 \)

Answer 2

oh ok. thank you. i want to ask a question to you.

Answer 3

sure, go ahead :)

Answer 4

the radius of a spherical balloon decreases at a rate of 0.3 cm/s. find the rate of change of the volume of balloon at the instant when the radius is 14 cm. (volume of sphere: (4/3)πr3 )

Answer 5

need to use a differentiation or not ???

Answer 6

so, we are given dr/dt = 0.3
yes, we need to differentiate.

Answer 7

ok, so what to do now.

Answer 8

rate of change of volume means we need dV/dt

so, differentiate V= 4/3 pi r^3
with respect to r
what do u get ?

Answer 9

wait

Answer 10

idk

Answer 11

sorry, differentiate V= 4/3 pi r^3
with respect to t ***

have you solved any differentiation sum before ?

Answer 12

i had

Answer 13

whats d/dx x^n = ... ?

Answer 14

n

Answer 15

no....
\(\Large \dfrac{d}{dx}x^n =n x^{n-1}\)
seen this ?

Answer 16

ohhhhh yes yes i forgot this xn−1

Answer 17

ok, so you know about chain rule ?

Answer 18

so-so only

Answer 19

ok, lets try to differentiate
V = 4/3 pi r^2
w.r.t 'r' then
what do u get ? try ?

Answer 20

***V = 4/3 pi r^3

Answer 21

wait, if i do like this.
dy= 4pir^2 x dx
= 4pi (14)^2 (0.3)

Answer 22

is it correct or not

Answer 23

yes, correct, just the notation is incorrect, but you will get correct final answer.

Answer 24

notation is incorrect ?

Answer 25

yes, its incorrect.
rate of change of volume =dV/dt
dV = change in volume
dt = change in time

Answer 26

ohhhh, i see it now.

Answer 27

decreases at a rate of 0.3 cm/s. ----- >dr/dt = -0.3


and you also forgot the negative sign

Answer 28

where

Answer 29

its -0.3 instead of 0.3
increases ----> +0.3
decreases----->-0.3

Answer 30

oh, idk it was like that. ok, here is my final answer.
235.2 pi

or is this the answer, 738.90

Answer 31

both are equivalent
-738.90 cm^3/s
or
-235.2pi cm^3/s

Answer 32

oh, i get it

Answer 33

cool :)

Answer 34

haha. thanks

Answer 35

welcome ^_^