An ice cream cone with a diameter of 2 inches and a height of 3.5 inches is filled with ice cream and more ice cream on top in the form of a hemisphere with the radius equal to the radius of the cone. Compute the total volume of ice cream it contains.

11pi/6 in^3 or

5.760 in^3 to the nearest thousandth.

Step-by-step explanation:

Volume of ice cream = volume of the cone + volume of the hemisphere

= 1/3 pi r^2 h + 1/2 * 4/3 pi r^3    

= 1/3 pi 1^2 * 3.5 + 2/3 pi 1^3             (as the radius = 1/2 * diameter)

=  (7/6 + 2/3) pi

= 11pi/6 in^3.

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.