Answer:
(a) 0.198 cm/s (b) 1 cm/s
Step-by-step explanation:
It is given that,
The rate of change of area of a cicle, [tex]\dfrac{dA}{dt}=5\ cm^2/s[/tex]
(a) The area of a circle is given by :
[tex]A=\pi r^2[/tex]
Differentiate both sides,
[tex]\dfrac{dA}{dt}=2\pi r\dfrac{dr}{dt}\\\\\text{Put the value of dA/dt and r = 4 cm}\\\\\dfrac{dr}{dt}=\dfrac{dA/dt}{2\pi r}\\\\\dfrac{dr}{dt}=\dfrac{5}{2\pi \times 4}\\\\\dfrac{dr}{dt}=0.198\ cm/s[/tex]
(b) Circumference, [tex]C=2\pi r[/tex] = 5 cm
[tex]\dfrac{dA}{dt}=2\pi r\dfrac{dr}{dt}\\\\\dfrac{dr}{dt}=\dfrac{dA/dt}{2\pi r}\\\\\dfrac{dr}{dt}=\dfrac{5}{5}\\\\\dfrac{dr}{dt}=1\ cm/s[/tex]
Hence,
(a) 0.198 cm/s (b) 1 cm/s
