If the radius of a circle is increasing at the constant rate of 2ft/sec, then the rate of increase of its area when the radius is 20ft is (in sq.ft/sec)
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The area of a circle (A) with radius (r) is given by,
A=πr
2
dt
dA
=
dt
d
(πr
2
)⋅
dt
dr
=2πr
dt
dr
, [By chain rule]
It is given that,
dt
dr
=3cm/s.
∴
dt
dA
=2πr(3)=6πr
Thus, when r=10cm,
∴
dt
dA
=6π(10)=60πcm
2
/s.
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