Answer: The length of the carton is 168 cm.
Step-by-step explanation: To find the length of the carton, we need to know how many tins fit along its width and height as well. Since we are not given this information, we will assume that the carton is packed in the most efficient way possible, which means that there are no gaps between the tins and that the tins are arranged in a hexagonal pattern. This pattern allows for the maximum number of circles to fit in a given area.
To find the width of the carton, we need to multiply the diameter of one tin by the number of tins along one row. The diameter of one tin is twice the radius, so it is 14 cm. The number of tins along one row is half the number of tins along the length, since each row is staggered by half a tin. Therefore, the number of tins along one row is 6. The width of the carton is then 14 cm x 6 = 84 cm.
To find the height of the carton, we need to multiply the height of one tin by the number of tins along one column. The height of one tin is 20 cm. The number of tins along one column is equal to the number of rows, which is determined by dividing the width of the carton by the distance between two adjacent rows. The distance between two adjacent rows is equal to the radius times √3, which is about 12.12 cm. Therefore, the number of rows is 84 cm / 12.12 cm ≈ 6.93. We round this up to 7, since we cannot have partial rows. The height of the carton is then 20 cm x 7 = 140 cm.
The length of the carton is already given as 12 times the diameter of one tin, which is 14 cm x 12 = 168 cm.
Therefore, the dimensions of the carton are:
Length: 168 cm
Width: 84 cm
Height: 140 cm
Hope this helps, and have a great day! =)