The number of cans that will fit the box is 694 cans.
Given:
Dimension of the cylindrical can of fish:
diameter (d) = [tex]76 mm = 7.6 cm (10 mm = 1 cm)[/tex]
radius (r) = [tex]\frac{1}{2}[/tex] of diameter = [tex]3.8 cm[/tex]
height (h) = [tex]10 mm = 1 cm[/tex]
Dimension of the box:
[tex]l = 36 cm\\b = 25cm\\h = 35cm[/tex]
Thus:
Number of cans that will fill the box = Volume of box / volume of 1 can
Volume of 1 can = volume of cylinder
Volume of cylinder = [tex]\pi r^{2} h[/tex]
Plug in the values
[tex]V = \pi \times 3.8^{2} \times 1\\V = 45.36cm^{3}[/tex]
Volume of box = [tex]l \times h \times b[/tex]
Plug in the values:
[tex]V = 36 \times 25 \times 35\\V = 31,500 cm^{3}[/tex]
Number of cans = [tex]\frac{31,500}{45.36} = 694.4[/tex]
Therefore, approximately 694 cans will fit in the box.
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