The radius of a circular disc is increasing at a constant rate of 0.003cm/s. Find the rate at which the area is increasing when the radius is 20cm.

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The rate at which the area is increasing, dA/dt, can be written with terms we know or can find out easily: dA/dt=dA/dr x dr/dt.

Area of a disc, A = (pi)r^2

dA/dr=2(pi)r

Rate of change of radius, dr/dt=0.003cm/s

Therefore, dA/dt=2(pi)r x 0.003

= 2(pi) x 20 x 0.003

=0.12(pi)

= 0.377cm^2/s

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