A spherical balloon is being inflated. find the rate of the surface area S= 4*pi*r^2 with respect to the radius r when r is a) 20 cm b)40 cm?

1 Answer
Nam D.
May 21, 2018

Refer to the explanation below.

Explanation:

We are given the surface area of the sphere as:

#S=4pir^2#

where:

  • #r# is the radius of the sphere

So the rate of change of the surface area of the sphere by its radius will be:

#(dS)/(dr)=8pir# by simple differentiation.

a) At #r=20 \ "cm"#, the rate of change will be #(dS)/(dr)=8pi*20 \ "cm"=160pi \ "cm"#.

b) At #r=40 \ "cm"#, the rate of change will be #(dS)/(dr)=8pi*40 \ "cm"=320pi \ "cm"#.

I'm not sure if my units are correct though, as the answer seems to have one-dimensional units, such as #"cm"# and not #"cm"^2#, as surface area is given in terms of #"cm"^2#.

Related questions
Impact of this question
17318 views around the world
You can reuse this answer
Creative Commons License