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Question
The rate of change of volume of a sphere with respect to its surface area, when the radius is 2 cm, is ______.
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Solution
The rate of change of volume of a sphere with respect to its surface area, when the radius is 2 cm, is 1.
Explanation:
1 cm3/cm2
v = `4/3 pi"r"^3`
⇒ `"dv"/"dr" = 4pi"r"^2`
s = `4pi"r"^2`
⇒ `"ds"/"dr"` = 8πr
⇒ `"dv"/"ds" = pi/2`
= 1 at r = 2.
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