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Bad White [126]
3 years ago
13

A circle is growing so that the radius is increasing at the rate of 2cm/min. How fast is the area of the circle changing at the

instant the radius is 10cm? Include units in your answer.
Mathematics
2 answers:
AnnyKZ [126]3 years ago
6 0
\bf \textit{area of a circle}\\\\
A=\pi r^2\qquad \qquad \implies \cfrac{dA}{dt}=\pi \cdot 2r\cdot \cfrac{dr}{dt}\impliedby chain-rule
\\\\\\
\begin{cases}
r=10\\
\frac{dr}{dt}=2
\end{cases}\qquad \cfrac{dA}{dt}=\pi \cdot 2(10)\cdot 2\implies \cfrac{dA}{dt}=40\pi~\frac{cm}{min}
poizon [28]3 years ago
5 0
The answer to this question is:

A circle is growing so that the radius is increasing at the rate of 2cm/min. How fast is the area of the circle changing at the instant the radius is 10cm? Include units in your answer.?
✔️I assume here the linear scale is changing at the rato of 5cm/min
✔️dR/dt=5(cm/min) (R - is the radius.... yrs, of the circle (not the side)
✔️The rate of area change would be d(pi*R^2)/dt=2pi*R*dR/dt. 
✔️At the instant when R=20cm,this rate would be, 
✔️2pi*20*5(cm^2/min)=200pi (cm^2/min)  or, almost, 628 (cm^2/min) 

Hoped This Helped, <span>Cello10
Your Welcome :) </span>
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