# Six spherical cannon balls are tightly packed into a rectangular box i

| Six spherical cannon balls are tightly packed into a rectangular box in one layer. Each row has two cannon balls and each column has three. What part of the box is empty?

A. 11/56

B. 10/21

C. 11/27

D. 5/21

### Right Answer is: B

#### SOLUTION

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=48r^{3}

Volume of 6 balls=6*(4/3)*(22/7)* r^{3}=176 r^{3}/7

The area of empty space=48 r^{3} -176 r^{3}/7

=160 r^{3}/7

The required fraction= (160 r^{3}/7)/48 r^{3}=10/21

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Six spherical cannon balls are tightly packed into a rectangular box i