Question

i really need help with this question ive been stuck on it for a while ...the volume of a spherical balloon is increasing at a constant rate of 5in^3/s. at what rate is the radius of the balloon increasing when its surface has area 16π in^2

Answer 1

what is the formula for the volume of a sphere? we need that to start

Answer 2

once we have that, this will take two steps to solve

Answer 3

4/3πr^2

Answer 4

ok so we have \[V(r)=\frac{4}{3}\pi r^3\]
\[V'(r)=4\pi r^2 r'\]
you are told \(V'(r)=5\) solve for \(r'\)

Answer 5

oh damn we also need \(r\) don't we. that is ok, we find the formula for the surface area and solve for \(r\) ok i lied it is 3 steps

Answer 6

surface area is 4πr^2 right?

Answer 7

\[S(r)=4\pi r^2\]
\[16\pi =4\pi r^2\]
\[4=r^2\]
\[r=2\] now we have \(r\)

Answer 8

and we have
\[5=4\pi r^2r'\] replace \(r\) by 2 get \[5=16\pi r'\] solve for \(r'\)

Answer 9

do you just minus 16 from both sides then minus π? im very confused at this point

Answer 10

how do i solve 5=16πr' for r'?