The radius of the base of a cone is increasing at the rate of `3 cm//min` and the altitude is decreasing at the rate of `4 cm//min`. The rate of change of lateral surface when the radius is `7 cm` and altitude is `24cm` is

Options

A. a) `108pi m^2//min`
B. (b) `7pic m^2//min`
C. c) `54pic m^2//min`
D. (d) None of these

Answer

c) `54pic m^2//min`

Explanation

Given, `r=7cm` and `h=24cm`


`l^2=r^2+h^2`
Slant height `(l)` `=sqrt(r^2+h^2)`


`l=sqrt(7^2+24^2)`


`l=sqrt(49+576)`


`l=sqrt(625)`


`l=25cm`


`l^2=r^2+h^2`



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