Stephenie puts 30 cubes in a box. The cubes are 1/2 inch on each side. The box holds 2 layers with 15 cubes in each layer. What is the volume of the box?
The Correct Answer and Explanation is:
Finding the Volume of the Box
To determine the volume of the box, let’s break the problem down systematically.
Step 1: Understand the cube size
Each cube has a side length of 1/2 inch (or 0.5 inches).
Step 2: Understand the arrangement
- The box holds 2 layers.
- Each layer contains 15 cubes.
- Total number of cubes: 30.
Step 3: Find dimensions of the box
Since the cubes are perfectly arranged in layers, the box dimensions must match the cubes’ total length in each direction.
- Height: Since there are 2 layers, the height is:
2×0.5=1 inch2 \times 0.5 = 1 \text{ inch}
- Width: Each layer contains 15 cubes arranged in a single layer. The width must be:
Assume a row of 5 cubes and a column of 3 cubes: 5×0.5=2.5 inches\text{Assume a row of 5 cubes and a column of 3 cubes: } 5 \times 0.5 = 2.5 \text{ inches}
- Depth: Since each layer has 3 rows, the depth must be:
3×0.5=1.5 inches3 \times 0.5 = 1.5 \text{ inches}
Step 4: Calculate Volume
The volume of a rectangular box is given by:
V=width×depth×heightV = \text{width} \times \text{depth} \times \text{height}
V=2.5×1.5×1=3.75 cubic inchesV = 2.5 \times 1.5 \times 1 = 3.75 \text{ cubic inches}
Explanation
Volume measures the space occupied by an object. Here, the volume of the box depends on its width, depth, and height, which are determined by the arrangement of cubes. Since each cube is 0.5 inches in size, multiplying the number of cubes in each direction gives the box’s dimensions. Thus, the correct answer is 3.75 cubic inches.
