The base of a rectangular box is 35 inches long and 20 inches wide. The height of the box is...
GMAT Geometry & Trigonometry : (Geo_Trig) Questions
The base of a rectangular box is \(35\) inches long and \(20\) inches wide. The height of the box is \(28\) inches. The box does not have a lid. What is the exterior surface area, in square inches, of this box without a lid?
Enter the integer value.
1. TRANSLATE the problem information
- Given information:
- Rectangular box: 35 inches long, 20 inches wide, 28 inches high
- Box has no lid (open at the top)
- Need exterior surface area
- What this tells us: We need to find the total area of all outside surfaces
2. INFER which surfaces to calculate
- Since there's no lid, the box has exactly 5 exterior surfaces:
- Bottom (base)
- Four vertical sides (front, back, left, right)
- Strategy: Calculate each surface area separately, then add them up
3. Calculate the base area
- Base dimensions: 35 inches × 20 inches
- Base area = \(35 \times 20 = 700\) square inches
4. Calculate the four vertical sides
- Two long sides (35 × 28):
- Each side area = \(35 \times 28 = 980\) square inches
- Total for both long sides = \(2 \times 980 = 1,960\) square inches
- Two short sides (20 × 28):
- Each side area = \(20 \times 28 = 560\) square inches
- Total for both short sides = \(2 \times 560 = 1,120\) square inches
5. SIMPLIFY by adding all surface areas
- Total surface area = base + long sides + short sides
- Total = \(700 + 1,960 + 1,120 = 3,780\) square inches
Answer: 3780
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret "without lid" and include a top surface in their calculation.
They calculate: base + top + four sides = \(700 + 700 + 1,960 + 1,120 = 4,480\) square inches
This leads to confusion since 4,480 isn't the correct answer, causing them to second-guess their work or abandon systematic solution.
Second Most Common Error:
Poor INFER reasoning: Students correctly identify that there's no lid but forget to include the base, thinking "exterior" means only the vertical sides.
They calculate: four sides only = \(1,960 + 1,120 = 3,080\) square inches
This also leads to getting an incorrect answer and potential guessing.
The Bottom Line:
This problem tests whether students can visualize a 3D object and systematically identify all its surfaces. The key insight is understanding that "exterior surface area without lid" means all outside surfaces except the top.