To determine how many round tins can fit in the box in a single layer, given that the dimensions of the box's bottom are 60 cm by 100 cm and each tin has a base area of 50 cm², we can follow these steps:
1. Calculate the area of the box's bottom:
- The bottom of the box is a rectangle with a length of 100 cm and a width of 60 cm.
- The area [tex]\(A_{box}\)[/tex] is given by the product of the length and the width.
[tex]\[
A_{box} = 100 \, \text{cm} \times 60 \, \text{cm} = 6000 \, \text{cm}^2
\][/tex]
2. Calculate the number of tins that can fit in the box:
- Each tin has a base area [tex]\(A_{tin} = 50 \, \text{cm}^2\)[/tex].
- To find out how many tins can fit within the box's bottom area, we divide the total area of the box by the area of one tin.
[tex]\[
\text{Number of tins} = \frac{A_{box}}{A_{tin}} = \frac{6000 \, \text{cm}^2}{50 \, \text{cm}^2} = 120
\][/tex]
3. Result:
- The number of tins that can fit in the box in a single layer is 120.
Therefore, 120 round tins will fit in the box in a single layer.
