20. Air is being pumped into a spherical balloon at a rate of 5 cm3 per minute. Determine the rate at which theradius of the balloon is increasing when the radius of the balloon is 20 cm. We know that the volume of asphere is given by V4.3Tr3124 (20)(rCC4 (20) (5)400X 2000 08000 TLem per minutc3e00X

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Asked Nov 9, 2019
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I got this wrong on my test, but I did it identical to an example we did in class. Where did I do wrong?

20. Air is being pumped into a spherical balloon at a rate of 5 cm3 per minute. Determine the rate at which the
radius of the balloon is increasing when the radius of the balloon is 20 cm. We know that the volume of a
sphere is given by V
4
.3
Tr
3
1
2
4 (20)(r
CC
4 (20) (5)
400
X 20
00 0
8000 TLem per minutc
3
e00X
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20. Air is being pumped into a spherical balloon at a rate of 5 cm3 per minute. Determine the rate at which the radius of the balloon is increasing when the radius of the balloon is 20 cm. We know that the volume of a sphere is given by V 4 .3 Tr 3 1 2 4 (20)(r CC 4 (20) (5) 400 X 20 00 0 8000 TLem per minutc 3 e00X

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Expert Answer

Step 1

Given:

Air is being pumped into a spherical balloon at a rate of 5 cm3/min. Determine the rate at which the radius of the balloon is increasing when the radius of the balloon is 20 cm.

Step 2

In this case we have given:

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Step 3

Now differentiating the Volume with respec...

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d(4 (V) dt 3 dt dV 4d 3 dt dt dr Зr2 dt dV 4т =_ dt 3 dV 47r2 dt dr dt 5 47(20) dt dr 5 dt 400 x 47 dr 1 dt 80x 477 dr 1 dt 3207

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Math

Calculus

Derivative