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Byju's Answer
Standard XII
Mathematics
Average Rate of Change
The volume of...
Question
The volume of a sphere is increasing at the rate of 3 cubic centimetre per second. Find the rate of its surface area, when the radius is 2cm.
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Solution
V
=
4
3
π
r
3
differentiating on both sides, we get,
d
V
d
t
=
4
π
r
2
d
r
d
t
⇒
d
r
d
t
=
1
4
π
r
2
d
V
d
t
r
=
2
c
m
,
d
V
d
t
=
3
c
m
2
/
s
e
c
∴
d
r
d
t
=
1
4
π
2
2
(
3
)
=
3
16
π
c
m
/
s
e
c
S
=
4
π
r
2
d
S
d
t
=
8
π
r
d
r
d
t
=
8
π
(
2
)
×
3
16
π
c
m
/
s
e
c
∴
d
S
d
t
=
3
c
m
2
/
s
e
c
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