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Application Of Derivatives

Question

Wired Faculty App

A circular disc of radius 3 cm is being heated. Due to expanison, its radius increases at the rate of 0.05 cm/s. Find the rate at which its area is increasing when radius is 3.2 cm.

Solution

Let r be the radius of the given disc and A be its area.

therefore space space space space space space space space space space space space straight A space equals space πr squared therefore space space space space space space dA over dt space equals space 2 πr dr over dt Now comma space approximate space rate space of space increase space of space radius space space equals space dr space equals space dr over dt increment straight t space equals space 0.05 space cm divided by straight s. therefore space space space the space approximate space rate space of space increase space in space area space is space given space by

dA space equals space dA over dt left parenthesis increment straight t right parenthesis space equals space 2 πr space open parentheses dr over dt increment straight t close parentheses space space space space space space space space equals space 2 straight pi left parenthesis 3.2 right parenthesis thin space left parenthesis 0.05 right parenthesis space space space space space space space space space equals space 0.320 space straight pi space cm squared divided by straight s space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space space space straight r space equals space 3.2 space cm close square brackets

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