\( \begin{array}{ll}\text { (a) } 100 \% & \text { (b) } 300 \% \\ \text { (c) } 500 \% & \text { (d) } 700 \%\end{array} \) 2. The length, width and height of a rectangular box are 10 cm 8 cm and 12 cm respectively. How many cubes of side 2 cm can be stacked in it? \( \begin{array}{ll}\text { (a) } 480 & \text { (b) } 240\end{array} \)
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To find out how many cubes of side 2 cm can fit inside the rectangular box with dimensions 10 cm, 8 cm, and 12 cm, we first calculate the volume of the box. The volume is given by: \[ \text{Volume of the box} = \text{length} \times \text{width} \times \text{height} = 10 \, \text{cm} \times 8 \, \text{cm} \times 12 \, \text{cm} = 960 \, \text{cm}^3 \] Next, we calculate the volume of one cube: \[ \text{Volume of one cube} = \text{side}^3 = 2\, \text{cm} \times 2 \, \text{cm} \times 2 \, \text{cm} = 8 \, \text{cm}^3 \] Now, to find out how many of these cubes can fit into the box, we divide the volume of the box by the volume of one cube: \[ \frac{960 \, \text{cm}^3}{8 \, \text{cm}^3} = 120 \] So, 120 cubes of side 2 cm can be stacked inside the box. However, none of the provided options match this answer. A common mistake here is miscalculation in understanding volume versus usable space. It’s vital to ensure each dimension of the box is adequately divisible by the cube’s side to optimize space effectively. For further study, you might explore volume and packing problems, which come up surprisingly often in fields such as logistics and design!
