Respuesta :
Considering balloon to be an spherical object
Volume of sphere = [tex]\frac{4}{3}\pi r^3[/tex], where r is the radius of sphere.
After 19 minutes ,If radius of balloon changes from r to R, the Volume changes from V to V'.
V'= [tex]\frac{4}{3}\pi R^3[/tex],
As given,rate at which the air leaked out of the balloon (in liters of air per minute) was half of the rate at which Vavilen inflated the balloon.
Also, [tex]\frac{dR}{dt}=2 \times \frac{dr}{dt}[/tex]
Now, again the radius changes from R to r.So, Volume changes from V' to Back to V.
Time taken by the balloon to deflate = 38 minutes
But there is no relation between time and volume of Balloon.
So, we can't predict at which rate balloon is deflating or inflating.Apart from the statement given in Question: [tex]\frac{dR}{dt}=2 \times \frac{dr}{dt}[/tex]
We can't predict at which rate the balloon is deflating or inflating. but we get the relation as [tex]\frac{dR}{dt} = 2 \times \frac{dr}{dt}[/tex].
What is the volume of a sphere?
A sphere is a three-dimensional shape analouge of a circle.
The volume of a sphere = 4/3πr^3
where r is the radius of the sphere.
Vavilen inflated a huge balloon in 19 minutes.
After 19 minutes, If the radius of the balloon changes from r to R, then the Volume also changes from V to V'.
Now, the rate at which the air leaked out of the balloon (in liters of air per minute) was half of the rate at which Vavilen inflated the balloon.
[tex]\frac{dR}{dt} = 2 \times \frac{dr}{dt}[/tex]
Again the radius changes from R to r. So the Volume changes from V to V'.
Time taken by the balloon to deflate = 38 minutes
But there is no relation between time and volume of Bthe alloon.
So, we can't predict at which rate the balloon is deflating or iinflating
Learn more about sphere;
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