Multiple choice

Sixteen cylindrical cans each with a radius of $1$ unit are placed inside a cardboard box four in a row. If the cans touch the adjacent cans and or the walls of the box, then which of the following could be the interior area of the bottom of the box in square units?

  1. $16$
  2. $32$
  3. $64$
  4. $128$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

16 cans, 4 in a row. This means a 4x4 grid of cans. Each can has radius 1, so diameter 2. The box must be 4*2 = 8 units wide and 4*2 = 8 units long. Area = 8 * 8 = 64.

AI explanation

With 4 cans placed in a row and each can having a radius of 1 unit, the length of the box needed to fit them is 4 times the diameter, which is 4 times 2 units giving 8 units. The arrangement of 16 cans requires 4 rows, making the interior width of the box 8 units as well. The area of the bottom of the box is 8 units times 8 units, giving 64 square units.

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