A new Action camera is sold in a box that is 5 cm high, 14 cm wide, and 24 cm long - Junior Cycle Mathematics - Question 2 - 2018

To determine the outside dimensions of the cover, we first need the dimensions of the combined 36 boxes.

• Height: For 36 boxes stacked,

  • Number of layers needed for height: $Height = 36 ext{ (single box height)} + 2 ext{ (for thickness)} = 4 imes 5 + 2 = 22 ext{ cm}$

• Width: $Width = 3 imes 14 + 2 = 44 ext{ cm}$

• Length: $Length = 3 imes 24 + 2 = 74 ext{ cm}$

Thus, the overall outside dimensions of the cover are:

• Height: 22 cm
• Width: 44 cm
• Length: 74 cm

To calculate the volume of plastic in the cover, we find the total volume of the outer dimensions and subtract the total volume of the boxes.

1. Total volume of the cover (external dimensions): $V_{cover} = Height imes Width imes Length = 22 imes 44 imes 74 = 70328 ext{ cm}³$

2. Total volume of the 36 boxes: $V_{boxes} = 36 imes 1680 = 60480 ext{ cm}³$

3. Volume of plastic in the cover: $V_{plastic} = V_{cover} - V_{boxes} = 70328 - 60480 = 9848 ext{ cm}³$

Thus, the volume of plastic in the cover is 9848 cm³.