Mathematics, 07.12.2019 14:31 HammondE

a gumball machine is in the shape of a sphere with a radius of 9 inches. a store manager wants to fill up the machine with gumballs, which have a radius of 3/4in. how many gumballs will fit in the machine?

547
1642
1728
5832

Answers: 2

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Answers

Answer from: Ericapab

Let's use the formula for spheres:
V= 4/3 pi*r^3

First find the volume of the machine.
V=4/3 pi 9^3
= 4/3 pi 729

I'm going to guess you need pi in decimal form: 3.141592

V= 4/3 * 3.14 * 729
approximately equal to 3052.08

Then find the volume of each gumball using the same formula:
V= 4/3 pi (3/4)^3
= 4/3 * 3.14 * 27/64
approximately equal to 1.77

Now you have the volume for one gumball.

Divide the volume of the machine by the volume of one gumball:

3052.08 / 1.77 = 1724.34

Now, that would usually be the answer, but you can't have 0.34 of a gumball! So round down to the whole number (1724) and there's your answer!

Also, keep in mind this is just an estimate since we're using 3.14 as pi. If you have a calculator with pi, you can plug that in and get a more accurate answer. So out of the options, I would say 1728 is the answer.

Hope this helps!

Answer from: Quest

a thesis statement is not a fact or a question

step-by-step explanation:

a thesis statement is a topic it is not a fact or a question

Answer from: Quest

la parábola es el lugar

geométrico en el cual los puntos tienen una distancia idéntica, equidistantes,

de un punto denominado foco, f, y una recta denominada directriz

el radio vector de una

parábola es el segmento que existe entre un punto cualquiera y el foco.

por la ecuación se observa

que la parábola abre hacia la derecha, por lo cual podemos usar las siguientes fórmulas

la ecuación ordinaria de la

parábola es y^2 = 4px, donde p es la longitud desde el vértice de la parábola al

foco.

la fórmula de la directriz

es x + p = 0

resolviendo:

y^2-9x = 0

y^2 = 9x

4p = 9, entonces p = 9/4

entonces el foco tendrá la

coordenada f(9/4,0)

la directriz vendrá

expresada por

x + p = 0

x = -p

x = -9/4

el problema indica que la

ordenada es igual a 6, entonces

(6)^2=9x

x = 36/9

x = 4

entonces el punto al cual

hay que obtener la distancia será p(4,6)

calculando se tendrá: pf =

pf = 6,25 u

ver más en -

step-by-step explanation:

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More questions: Mathematics Another questions

a gumball machine is in the shape of a sphere with a radius of 9 inches. a store manager wants to fill up the machine with gumballs, which have a radius of 3/4in. how many gumballs will fit in the machine? 547 1642 1728 5832

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Another question on Mathematics

a gumball machine is in the shape of a sphere with a radius of 9 inches. a store manager wants to fill up the machine with gumballs, which have a radius of 3/4in. how many gumballs will fit in the machine?

547
1642
1728
5832