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A rectangular box tightly packed with six spherical cannon plastic balls in one layer. Each row has two cannon balls and each column has three. What part of the box is empty?

A rectangular box tightly packed with six spherical cannon plastic balls in one layer. Each row has two cannon balls and each column has three. What part of the box is empty? Correct Answer 10/21

Given:

In rectangular box each row has two cannon balls and each column has three

Formula:

Volume of cuboid = L × B × H

Volume of sphere  =4/3 × π × r3

Calculations:

Let the diameter of each ball be 2r.

Length of the box = 3 × 2r = 6r

Breadth = 2 × 2r = 4r

Height = 2r

Volume = 6r × 4r × 2r = 48r3

Volume of 6 balls = 6 × (4/3)(22/7)r3  = (176 r3/7)

The area of empty space = 48 r3 - (176 r3/7)

⇒ (160 r3/7)

The required fraction = (160 r3/7)/(48r3)

⇒ (10/21)

∴ 10/21 part of the box is empty

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