A spherical balloon is inflating with helium at a rate of 64 pi StartFraction ft cubed Over min EndFraction . How fast is the b
alloon's radius increasing at the instant the radius is 2 ft?
1 answer:
Answer:
The radius of the balloon is increasing at a rate of 4 feet per minute.
Step-by-step explanation:
We are given the following in the question:

Volume of sphere is given by

where r is the radius of the balloon.
Instant radius, r = 2 ft
Rate of change of volume =

Putting values, we get,

Thus, the radius of the balloon is increasing at a rate of 4 feet per minute.
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Answer:
1) 
2) 
3) 
4) 
Step-by-step explanation:
1) 
Solving using exponent rule: 

So, 
2) 
Using the exponent rule: 
We have:

We also know that: 
Using this rule:

So, 
3) 
Solving:

So, 
4) 
We know that: 

So, 