applications of calculus question (1 Viewer)

someonehomebush · Oct 7, 2011

Can someone provide the step by step solutions to solve this question please?

A circular metal plate of radius r is heated so that its area expands at a constant rate of 4cm^2/min. At what rate does the radius increase when r=10 cm?

The book says the answer is 0.064 cm/min

SpiralFlex · Oct 7, 2011

someonehomebush said:
Can someone provide the step by step solutions to solve this question please?

A circular metal plate of radius r is heated so that its area expands at a constant rate of 4cm^2/min. At what rate does the radius increase when r=10 cm?

The book says the answer is 0.064 cm/min

We have to understand that the area of a circular metal plate is given by,

$A=\pi r^2$

$\therefore \frac{dA}{dr}=2\pi r$

Using the chain rule,

$\frac{dA}{dt}=\frac{dA}{dr}*\frac{dr}{dt}$

$4=\2 \pi r *\frac{dr}{dt}$

When $r=10$

$4=\2 \pi *10 *\frac{dr}{dt}$

$\therefore \frac{dr}{dt}= 0.064 \: \textup{cm/min}$

someth1ng · Oct 7, 2011

SpiralSex has done it again!

SpiralFlex · Oct 7, 2011

Please do not use my name in such demonstrative fashion.

applications of calculus question (1 Viewer)

someonehomebush

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