A rectangular box is 4cm wide, 4cm tall, and 10cm long. What is the diameter of the smallest circular opening through which the box will fit? Round to the nearest tenth of a centimeter. Is it 4 squared plus 4 squared which equals 32 then take the square root of 32 and get 5.65 or 5.7.
Sliding the box through the circle length wise means that the circle must be able to at least as long as the diagonal.
So you are right,
D^2 = 4^2 + 4^2 = 32
D = √32 = appr 5.7
To find the diameter of the smallest circular opening through which the box will fit, you need to consider the diagonal of the box. Using the Pythagorean theorem, you correctly found the diagonal of one side of the box by calculating the square root of (4 squared + 4 squared), which equals 5.65 or 5.7 when rounded to the nearest tenth.
However, since the opening needs to accommodate the entirety of the box, you must consider the diagonal of the base of the box as well. You can calculate this by using the Pythagorean theorem once again. The diagonal of the base is the square root of (4 squared + 10 squared), which equals 10.77 or 10.8 when rounded to the nearest tenth.
Since the smallest circular opening must fit the diagonal of the base, which is larger than the diagonal of one side, the correct answer would be 10.8 cm when rounded to the nearest tenth.