Question

part B please

The area of a circle increases at a rate of 6 cm /s. a. How fast is the radius changing when the radius is 1 cm? b. How fast is the radius changing when the circumference is 2 cm?

Answer 1

(b)

Area of a circle having radius r is given by

$A=\pi r^{2}$

$\frac{\mathrm{d} A}{\mathrm{d} t}=6$

t is time in seconds.

Circumference of a circle having radius r is given by

circumference = 277

ДА dt 2 7T7" dt

$=\pi \times \frac{\mathrm{d} }{\mathrm{d} t}\left [ r^{2} \right ]$

$=\pi \times 2r\frac{\mathrm{d} r}{\mathrm{d} t}$

$=2\pi r\frac{\mathrm{d} r}{\mathrm{d} t}$

$\frac{\mathrm{d} A}{\mathrm{d} t}=6$

$\Rightarrow 2\pi r\frac{\mathrm{d} r}{\mathrm{d} t}=6$

$\frac{\mathrm{d} r}{\mathrm{d} t}=\frac{6}{2\pi r}=\frac{6}{circumference}$

When circumference is 2 cm, rate of change of radius is given by

$\frac{\mathrm{d} r}{\mathrm{d} t}=\frac{6}{circumference}=\frac{6}{2}=3$

That is

Radius is increasing at a rate of 3 cm/s.

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