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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.

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FamousJay
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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, Cello10
Your Welcome :) 

The area of the circle changing at the instant the radius is 80π cm²/min

What is the area of a circle?

The area of a circle is defined as the space occupied by the circle in a two-dimensional plane. In other word, the space occupied under the region or circumference of a circle is called the area of the circle.

The formula for the area of a circle is A = πr²,

Where r is the radius of the circle.

For example, if the radius of circle is 6cm, then its area will be: Area of circle with 6 cm radius = πr² = π(6)² = 36π square cm.

Given that,

Radius of the circle (r) = 10cm

The rate of changing of circle (dr/dt) = 2 cm/min

If A= the area of the circle

we determine =  [dA/dt]r

According to the chain rule,

dA/dt = dr/dt × dA/dr

Now for a circle

Area of circle = πr²

⇒dA/dr = 2πr

Substitute the value of r = 10

⇒ dA/dr = 2π×10 = 20π       [dr/dt = 2]

⇒ dA/dr = 2 × 40π = 80π cm²/min

Hence, the area of the circle changing at the instant the radius is 80π cm²/min

Learn more about area of the circle here:

https://brainly.com/question/11952845

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