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A packaging company wants to fit 6 energy drink cans in a cardboard box, as shown below. The

bottom of each can is a circle with a radius of 4 cm. What is the area of the bottom of the box not
taken up (left over) by the cans?

1 Answer

1 vote

Answer:


\bigtriangleup A\approx 82.41\ cm^2

Explanation:

-Assume the cans are arranged in a two by three dimensions.

-Therefore the length of the box is equivalent to 3 diameters and the width is equivalent to two diameters:


D=2r=2* 4=8\ cm\\\\Length=3D=3* 8=24\\\\Width=2D=2* 8=16
cm

#The area of the cardboard box is calculated as:


Area=lw\\\\=24* 16\\\\=384\ cm^2

#The total bottom areas of the 6 cans is:


A_6=6\pi r^2\\\\=6\pi * 4^2\\\\=301.593\ cm^2

#The area not covered is the difference between the area of the box and the total bottom areas of the 6 cans:


\bigtriangleup A=A_b-A_c\\\\=384-301.593\\\\=82.407\ cm^2\\\\\approx 82.41\ cm^2

Hence, the area not covered is approximately
82.41\ cm^2

*Note that whichever order of arrangement the cans assume, the areas of the boxes will be the same.

User Eric Lechner
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