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Standard X
Mathematics
Circumference
The radius of...
Question
The radius of a circle is increasing at the rate of 0.5 cm/sec. Find the rate of increase of its circumference.
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Solution
Let
r
be the radius and
C
be the circumference of the circle at any time
t.
Then,
C
=
2
π
r
⇒
d
C
d
t
=
2
π
d
r
d
t
⇒
d
C
d
t
=
2
π
×
0
.
5
∵
d
r
d
t
=0.5 cm/sec
⇒
d
C
d
t
=
π
cm
/
sec
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