Find the rate of change of the total surface | vedclass

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(B) The total surface area $A$ of a cylinder is given by the formula: $A = 2 \pi rh + 2 \pi r^2$.To find the rate of change of $A$ with respect to tim

Vedclass · Accepted Answer

$(4 \pi r + 2 \pi h) \frac{dr}{dt}$

Vedclass · Answer

(B) The total surface area $A$ of a cylinder is given by the formula: $A = 2 \pi rh + 2 \pi r^2$.To find the rate of change of $A$ with respect to time $t$,we differentiate both sides with respect to $t$ using the product rule and chain rule:$\frac{dA}{dt} = \frac{d}{dt}(2 \pi rh) + \frac{d}{dt}(2 \pi r^2)$Assuming height $h$ is constant,we get:$\frac{dA}{dt} = 2 \pi h \frac{dr}{dt} + 4 \pi r \frac{dr}{dt}$Factoring out the common terms,we obtain:$\frac{dA}{dt} = (2 \pi h + 4 \pi r) \frac{dr}{dt}$.

Find the rate of change of the total surface area of a cylinder of radius $r$ and height $h$,when the radius varies with respect to time $t$.

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