Write your question here... The radius of a circular disc is increasing at the rate of 0.5 cm/sec. Ar what rate is the area of the disc increasing when its radius is 6cm?

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Answer 1 · 2018-02-18T17:05:50

Rate of change in area with respect to time is
#(dA)/dt=6*pi#

Let area of disc be A cm^2 and it's radius be r cm,
Then,
#A=pi*r^2#
Differentiating with respect to time,

#(dA)/dt=2*pi*r*(dr)/dt#

From the question, we can infer that,
#(dr)/dt=0.5, r=6#

Substituting these values in equation,

#(dA)/dt=2*pi*6*0.5#

#(dA)/dt=6*pi#

Thus, rate of change of area is #6*pi#