A storage bin in the corner of Joe’s room has the dimensions shown below. What is the volume of the bin? 5 feet 2 feet 2 feet 2 feet 4 feet 3 feet 2 feet
The Correct Answer and Explanation is:
To find the volume of the storage bin, we must recognize that the shape can be divided into two rectangular prisms.
Step 1: Divide the figure
The bin is shaped like an L, so we can divide it into two rectangular parts:
- Prism A (taller section):
- Dimensions: 2 ft (width) × 3 ft (length) × 5 ft (height)
- Volume = 2 × 3 × 5 = 30 cubic feet
- Prism B (shorter section):
- Dimensions: 2 ft (width) × 4 ft (length) × 2 ft (height)
- Volume = 2 × 4 × 2 = 16 cubic feet
Step 2: Add the volumes
Total volume = Volume of Prism A + Volume of Prism B
Total volume = 30 + 16 = 46 cubic feet
Explanation
To determine the volume of a 3D object, you use the formula for the volume of a rectangular prism:
Volume = length × width × height
The bin shown in the diagram is not a simple rectangular box but an L-shaped object. When faced with composite shapes like this, the best strategy is to divide the shape into smaller, manageable rectangular prisms.
Looking at the diagram, you can see that the L-shape is made from two rectangles joined at a corner. The taller part is clearly defined with a height of 5 feet, a depth of 2 feet, and a visible front width of 3 feet. This makes the first prism (Prism A).
The second part, or Prism B, lies flat next to the tall one, with dimensions labeled clearly as 2 feet tall, 2 feet wide, and 4 feet long.
After calculating the volume of each prism, we add the two volumes together because volume is additive when combining solid objects with no overlap. This method ensures accuracy without trying to use complex geometry formulas.
Thus, by splitting the shape and applying the basic volume formula to each part, we find that the total volume of the storage bin is:
46 cubic feet.
