A sphérical báll of salt is dissolving in water in such a manner that the ráte of décrease of the volume at any iñstant is propôrtional to the surface. Prove that the radius is decréasing at a coñstant rate.
Answers
Answered by
1
Answer:
According to the question
d t
d V
= K×(surface area)
V=
3
4
πr
3
,SA= 4πr
2
dt
d (
3
4
πr
3
)
= K× 4πr
2
3
4π
dt
dr
3
= 4πKr
2
3
4π
× 3r
2
×
dt
dr
= 4πKr
2
dt
dr
= K
Hence true.
Answered by
1
Answer:
According to the question
d t
d V
= K×(surface area)
V=
3
4
πr
3
,SA= 4πr
2
dt
d (
3
4
πr
3
)
= K× 4πr
2
3
4π
dt
dr
3
= 4πKr
2
3
4π
× 3r
2
×
dt
dr
= 4πKr
2
dt
dr
= K
Hence true.
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