SOLUTION: Help me please A spherical balloon is decreasing its volume at a rate of 163.87 cm3/min. Find the rate at which the radius is decreasing when the volume is 4916.12 cm3. Roun

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Question 1163170: Help me please
A spherical balloon is decreasing its volume at a rate of 163.87 cm3/min. Find the rate at which the radius is decreasing when the volume is 4916.12 cm3.
Round to 5 significant digits.
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




is given.





for given :



So:



You are given and . Plug in the numbers and do the arithmetic.

Note: Volume is measured in cubic centimeters and the radius is measured in centimeters. The time unit is minutes.


John

My calculator said it, I believe it, that settles it

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Instead of doing it for you, I'll do another one exactly like yours with the
numbers changed.  I'll do this one:

A spherical balloon is decreasing its volume at a rate of 274.98 cm³/min.
Find the rate at which the radius is decreasing when the volume is 5027.23
cm³.
Round to 5 significant digits.
V+=+expr%284%2F3%29pi%2Ar%5E3

V+=+4.188790205r%5E3

When the volume is 5027.23 cm³, the radius is

5027.23+=+4.188790205r%5E3

5027.23%2F4.188790205=r%5E3

1200.162757=r%5E3

root%283%2C1200.162757%29=r

10.6270661=r

Now go back to the formula, allowing r and V to vary.

V+=+4.188790205r%5E3

dV%2Fdt=3%2A4.188790205r%5E2%2Aexpr%28dr%2Fdt%29

dV%2Fdt=12.56637062r%5E2%2Aexpr%28dr%2Fdt%29

Now substitute the values:

274.98=12.56637062%2810.6270661%29%5E2%2Aexpr%28dr%2Fdt%29

274.98=1419.177209%2Aexpr%28dr%2Fdt%29

274.98%2F1419.177209=dr%2Fdt

0.19376=dr%2Fdt

Answer for my problem: 0.19376 cm²/min

Now do yours.

Edwin