A)
Given: dr/dt = .03 m/s and r = 18 m
Volume of a sphere = (4/3)*PI*r^3
Take the derivative of both sides, so
dv/dt = 4*PI*r^2*dr/dt
Plug in the givens and you have the rate of increase of the volume
B)
Given: V = 288 m^3 and I'm going to assume that r and dr/dt are the same as in part A
Surface Area = 4*PI*r^2
Take the derivative on both sides, so
dA/dt = 8*PI*r*dr/dt
Again, plug in the givens and you'll have the rate of increase in the surface area
C)
This part, it's been awhile since I've done related rates, so it may take me awhile, but perhaps the next person can answer it before I finish.
Answer:47.725%
If the mean (μ) is 80, and the standard deviation (σ) is 5, then all scores between 80 and 90 would fall between 0 and 2 standard deviations above the mean.
Using the equation for Z score (Z = (X-μ)/σ) for each X value (80 and 90) then the Z scores are 0 and 2, respectively.
Using a normal distribution table, it can be found that P(80 < z) = .5 (this is the probability that a random score would be greater than 80. It makes sense that it is .5 or 50% because 80 is the mean.)
And the P(90 > z) = .97725. (this is the probability that a random score would be less than 90.)
