Homework Help

Using linear approximations, if a spherical ballon has a radius of 5 cm, find the...

user profile pic

karengervasi | Student | eNoter

Posted July 2, 2013 at 9:48 AM via iOS

dislike 1 like

Using linear approximations, if a spherical ballon has a radius of 5 cm, find the increase in volume of the balloon when the radius expands by 0.02 cm

1 Answer | Add Yours

user profile pic

aruv | High School Teacher | Valedictorian

Posted July 2, 2013 at 10:39 AM (Answer #1)

dislike 1 like

Let volume of the sphere of radius r be V

Thus

`V=(4/3)pir^3`

`(dV)/(dr)=4pir^2`

`But`

`DeltaV=(dV)/(dr)Deltar`

`` because

`lim_(Deltar->0)(DeltaV)/(Deltar)=(dV)/(dr)`

`Thus`

`DeltaV=(4pir^2)Deltar`

`DeltaV=` Change in volume

`Deltar=`  Change in radius

Thus

`r=5`

`Deltar=.02`

`DeltaV=(4xx3.14xx5^2)xx.02`

`DeltaV=314xx.02`

`DeltaV=0.0628`  cubic cm

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes