A spherical party balloon is being inflated with helium pumped in at a rate of 10 cubic feet per minute. How fast is the radius growing at the instant when the radius has reached 1 ft? HINT [See Example 1.] (The volume of a sphere of radius r is V = 4/3 πr3. Round your answer to two decimal places.)

The radius is growing at a rate of   ft per minute.

Step-by-step explanation:

From the information given we know that

And we know as well that .

Since everything is changing with the time we can compute the implicit  derivative and we would get that

We are told that we are looking for how fast is the radius growing at the instant when the radius has reached 1 ft, therefore  

And when we solve for  

answer: the answer is 35%

answer: the answer is 30 miles per hour.

ft/s -> mphmph = ft/s 1.466667mph = 44 divided by 1.466667mph = 30.00000

- r3ktforgood ☕