Q1. [3] § 12.3 Volume of a Combination of Solids
To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted by semi-cylinder as shown in the figure. Find the area of the cloth required to make this shed, if dimensions of the cuboid are $14\ \text{m} \times 25\ \text{m} \times 16\ \text{m}$.
Previously asked in CBSE board exam
2026 30/4/1 Q29 (OR-1)
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer
Given: Cuboid: 14 m × 25 m × 16 m; Semi-cylinder mounted on top (diameter = 14 m, so radius = 7 m, length = 25 m)
The cloth covers:
- Two side walls of cuboid (excluding top): 2 × (25 × 16) = 800 m²
- Two end walls (rectangles minus semicircles) + two semicircular ends of cylinder:
2 × (14 × 16) + 2 × ½πr² = 448 + 22/7 × 7 × 7 = 448 + 154 = 602 m²
- Curved surface of semi-cylinder: πrl = 22/7 × 7 × 25 = 550 m²
Total area of cloth = 800 + 602 + 550 = 1952 m²
Source: Surface Area of a Combination of Solids, Chapter 12, Section 12.2
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Explanation
- The top face of the cuboid is replaced by the semi-cylinder, so it is not included.
- The two end walls are rectangles (14 × 16) each, but the semi-circular portion at the top of each end is part of the semi-cylinder's flat ends — add two semicircles (= one full circle = πr²).
- The curved surface of the semi-cylinder = ½ × 2πrl = πrl.
- Examiner expects all three components identified and added correctly. Show each step clearly for full marks.
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