The variation of radius of a circle with time is given by the relation r = (20 + 3) m, where t is time in second. The rate of change of area of the circle at t = 1 s will be
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Explanation:
(i) The area of a circle (A) with radius (r) is given by,
A=πr
2
Now, the rate of change of the area with respect to its radius is given by,
dr
dA
=
dr
d
(πr
2
)=2πr
At r=3 cm,
dr
dA
=2π(3)=6π
(ii)
The area of a circle (A) with radius (r) is given by,
A=πr
2
Now, the rate of change of the area with respect to its radius is given by,
dr
dA
=
dr
d
(πr
2
)=2πr
At r=4 cm,
dr
dA
=2π(4)=8π
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