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:
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