A circle with a radius of 5cm has it radius increasing at the rate of 0.2cm/s. What will be the corresponding increase in the area?
3 answers
rate of area increase = circumference * rate of radius increase = 2π cm^2/s
Its good
r=5cm; dr/dt=0.2cm/s
Area of Circle, A=πr²
Required to find: Increase in area=dA/dt
dA/dt= (dA/dr) x (dr/dt)
But dA/dr=2πr
Hence,
dA/dt=(2πr) x (0.2)
=0.4πr
Since r=5cm,
dA/dt=0.4π x 5
=2π cm²/s
Area of Circle, A=πr²
Required to find: Increase in area=dA/dt
dA/dt= (dA/dr) x (dr/dt)
But dA/dr=2πr
Hence,
dA/dt=(2πr) x (0.2)
=0.4πr
Since r=5cm,
dA/dt=0.4π x 5
=2π cm²/s