Question

The radius of a spherical balloon is increasing at the rate of 0.6 cm divided by minute. How fast is the volume changing when the radius is 7.5 ​cm? The volume is changing at a rate of nothing cm cubed divided by minute. ​(Type an integer or a decimal. Round to one decimal place as​ needed.)

Answer 1

`(dV)/(dt) =424.12\ cm^3/min`

Step-by-step explanation:

given,

radius increasing rate = 0.6 cm/minute

the volume changing when the radius = 7.5 ​cm

volume of the sphere=
`(4)/(3)\pi r^3`

`(dr)/(dt) = 0.6 cm/min`

`V =(4)/(3)\pi r^3`

`(dV)/(dt) =(4)/(3)\pi (3r^2)(dr)/(dt)`

`(dV)/(dt) =4\pi r^2(dr)/(dt)`

`(dV)/(dt) =4\pi 7.5^2* 0.6`

`(dV)/(dt) =424.12\ cm^3/min`