Finding a rate of sphere area increase given its volume increaseVolume of sphere, V =...

Lilliana Livingston

Lilliana Livingston

Answered

2022-07-18

Finding a rate of sphere area increase given its volume increase
Volume of sphere, V = 4 3 π r 3
Surface area of sphere S = 4 π r 2 .
If we know, d V d t = R.
Let us consider both volume and area as composite functions, thus d V d t = d V d r × d r d t = 4 π r 2 × d r d t = R
whence d r d t = R 4 π r 2 since d S d t = 6 π r d r d t , let the value of the d r d t into the second equation, to get the answer. Is this approach logically correct?

Answer & Explanation

Steppkelk

Steppkelk

Expert

2022-07-19Added 11 answers

Step 1
Everything is fine until you did
whence d r d t = R 4 π r 2 since d S d t = 6 π r d r d t .
d S d t = 8 π r d r d t
Step 2
Therefore d S d t = 8 π r R 4 π r 2
and finally d S d t = 2 R r

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