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Test Index
JEE Main Math Class 12 Application of Derivatives Part 1 Questions
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© examsnet.com
Question : 1
Total: 100
A spherical iron ball of radius 10 cm is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm
3
/min. When the thickness of the ice is 5 cm, then the rate at which the thickness (in cm/min) of the ice decreases, is :
[April 10, 2019 (II)]
1
18
π
1
36
π
5
6
π
1
9
π
Validate
Solution:
Given that ice melts at a rate of
50
c
m
3
∕
m
i
n
.
∴
d
V
ice
d
t
=
50
V
ice
=
4
3
π
(
10
+
r
)
3
−
4
3
π
(
10
)
3
⇒
d
V
d
t
=
4
3
π
3
(
10
+
r
)
2
d
r
d
t
=
4
π
(
10
+
r
)
2
d
r
d
t
Substitute r = 5,
50
=
4
π
(
225
)
d
r
d
t
⇒
d
r
d
t
=
50
4
π
(
225
)
=
1
18
π
c
m
∕
m
i
n
© examsnet.com
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