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A stock person at a local department store decided that they would like to completely fill the ball bin in the toy department with one type of ball. the ball the stock person decided to use has a radius of 16 cm. the bal bin is 210 cm tall and the opening at the top is a square that is 150 cm by 150 cm. how many balls should fit inside the bin? (reminder: you can assume that for random packing space 190% of the volume of the sphere is needed to pack the spheres and ) group of answer choices

Respuesta :

145 balls would fit inside the bin.

Given:

The radius of the ball (r) = 16 cm

The height of the ball bin  = 210 cm

The opening at the top is a square that is 150 cm × 150 cm.

The side length of the square ball bin = 150 cm

To Find:

How many balls should fit inside the bin = ?

First we find the volume of the ball.

Let the volume of the ball be V1

The volume of the sphere = 4/3 × π × r³

Substituting the value,

⇒ V1 = 4/3 × π × 16³

⇒ V1 = 4/3 × π × 4096

⇒ V1 = (16348 × π) / 3

⇒ V1 = 17157.3 cubic centimeters

Now, we find the packing space per ball

= 190 percent of volume of one ball

= 190% of 17157.3

= 190/100 × 17157.3

= 1.9 × 17157.3

= 32598.9 cubic cm

Now, we find the volume of the container

The volume of the square prism (packing box )

= base area × height

= area of square × height

= 150² × 210

= 4725000 cubic centimeters

Now, we find the number of ball that can fit in the container

Number of ball = volume of the container / the packing space per ball

so,

⇒ Number of ball = 4725000 /  32598.9

⇒ Number of ball = 144.9

⇒ Number of ball ≈ 145

This means, approximately 145 balls should fit inside the bin.

Therefore, 145 balls would fit inside the bin.

Learn more about the volume of the sphere here:

https://brainly.com/question/24420115

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