A scoop of ice cream, shaped like a sphere with diameter 6 cm, is
placed in an ice cream cone with diameter 5 cm and height 9 cm.
Is the cone big enough to hold all the ice cream if it melts? Explain.

The answer is no.

We need to calculate if the volume of the ice cream is equal or smaller than the volume of the ice cream cone.

The volume of the ice cream (sphere) is

V1 = 4/3 r³ π

d =  6

r = d/2 = 6/2 = 3

V1 = 4/3 * 3³ * 3.14 = 113.04 cm³

The volume of the ice cream cone is:

V2 = 1/3 r² h π

d = 5

r = d/2 = 5/2 = 2.5

h = 12

V2 = 1/3 * 2.5² * 12 * 3.14 = 78.5 cm³

Since the volume of the ice cream (V1) is bigger than the volume of the ice cream cone (V2), the cone is not big enough to hold all the ice cream if it melts

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the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )