Designer Furnishings sells premade cabinets and cupboards, as shown below.
| Model | Dimensions (in inches) |
| :------ | :--------------------- |
| 411 R | 32 by 22 by 10 |
| 412 R | 28 by 36 by 15 |
| 413 S | 24 by 72 by 18 |
| 414 S | 25 by 24 by 6 |
Each face of cabinet 413 S is in the shape of a rectangle. What is the volume, in cubic feet, of Model 413S?
A. 18
B. 31
C. 36
D. 108
Answer (2)
Convert the dimensions from inches to feet: Length = 12 24 = 2 feet, Width = 12 72 = 6 feet, Height = 12 18 = 1.5 feet.
Calculate the volume by multiplying the converted dimensions: Volume = 2 × 6 × 1.5 .
The volume is 18 cubic feet.
The volume of Model 413S is 18 .
Explanation
Problem Analysis The problem provides the dimensions of cabinet 413S in inches and asks for the volume in cubic feet. The dimensions are 24 inches, 72 inches, and 18 inches. To find the volume in cubic feet, we first need to convert the dimensions from inches to feet and then multiply them together.
Convert inches to feet First, convert the length from inches to feet. Since there are 12 inches in a foot, we divide the length in inches by 12: Length in feet = 12 inches/foot 24 inches = 2 feet Next, convert the width from inches to feet: Width in feet = 12 inches/foot 72 inches = 6 feet Then, convert the height from inches to feet: Height in feet = 12 inches/foot 18 inches = 1.5 feet
Calculate the volume Now that we have the dimensions in feet, we can calculate the volume in cubic feet by multiplying the length, width, and height: Volume = Length × Width × Height = 2 feet × 6 feet × 1.5 feet = 18 cubic feet
Final Answer The volume of Model 413S is 18 cubic feet.
Examples
Understanding volume is crucial in many real-world scenarios. For instance, when planning a move, knowing the volume of your boxes and the storage space helps you determine the right size of the moving truck or storage unit needed. Similarly, in construction, calculating the volume of materials like concrete is essential for accurate ordering and cost estimation. In packaging and shipping, volume calculations ensure efficient use of space and help optimize transportation costs.
The volume of Model 413 S is calculated by converting the dimensions from inches to feet and multiplying them together. The final volume is 18 cubic feet, which corresponds to option A. Therefore, the correct answer is A. 18.
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