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(b]1. Homework Statement [/b]

A spherical weather balloon has a radius of 1m when it is 1500m high.

You observe that the radius increases at a rate of 2cm/min as it continues to rise.

At what rate is the surface area increasing when the radius is 4m?

I thought volume of a sphere might be useful to help solve this question.

V = 4/3pi(r^3)

I was not sure if the first sentence of the question could help me solve this problem or not, so i decided to try and solve it without using the info from there.

It looks like from the given information that the following might be the case:

if i let r be the radius then r = 4

the rate at which the radius increases with respect to time could be shown as:

dr/dt = 2

Now, this is where i get stuck; i am not sure if i am correct in making my next step to differentiate the volume of a sphere function, but this is what i arrived at:

if V=4/3pi(r^3)

THEN

dV/dt=4pi(r^2)

I am stuck at this point, because i don't know how to take it further, help please?

A spherical weather balloon has a radius of 1m when it is 1500m high.

You observe that the radius increases at a rate of 2cm/min as it continues to rise.

At what rate is the surface area increasing when the radius is 4m?

## Homework Equations

I thought volume of a sphere might be useful to help solve this question.

V = 4/3pi(r^3)

## The Attempt at a Solution

I was not sure if the first sentence of the question could help me solve this problem or not, so i decided to try and solve it without using the info from there.

It looks like from the given information that the following might be the case:

if i let r be the radius then r = 4

the rate at which the radius increases with respect to time could be shown as:

dr/dt = 2

Now, this is where i get stuck; i am not sure if i am correct in making my next step to differentiate the volume of a sphere function, but this is what i arrived at:

if V=4/3pi(r^3)

THEN

dV/dt=4pi(r^2)

I am stuck at this point, because i don't know how to take it further, help please?

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