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Aleks [24]
2 years ago
12

A cylinder has a height of 8.1 inches and circular base with a diameter of 2.7 inches. The cylinder contains 3 green spheres, ea

ch having a diameter of 2.7 inches.
If a point is chosen at random inside the cylinder, then what’s the probability the point belongs outside of the spheres. Show all work necessary.
Mathematics
1 answer:
klasskru [66]2 years ago
6 0

Answer:

A point is chosen at random inside the cylinder, then probability the point belongs outside of the spheres is 0.25

Step-by-step explanation:

Let's find volume of the cylinder and volume of the three spheres.

Volume of cylinder =\pi r^{2} h

Volume of sphere =\frac{4}{3} \pi r^{3}

Now, r =2.7

h=8.1

Find volume of each shape.

Volume of cylinder =\pi (2.7)^{2} (8.1)

                             =59.049\pi

Now, volume of 3 spheres =3*\frac{4}{3} *\pi *(2.7)^{3}

                                         =78.732\pi

Now, p(E)=\frac{Outcomes favorable to event E}{Total number of outcomes}

So, Probability of point is chosen at random inside the cylinder which belongs outside of the spheres  is

                  \frac{78.732\pi -59.049\pi }{78.732\pi }

Let's simplify them

             0.25

A point is chosen at random inside the cylinder, then probability the point belongs outside of the spheres is 0.25

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