A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 5·8 cm and its base is of radius 2·1 cm, find the total surface area of the article.
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer
Given: Height of cylinder (h) = 5.8 cm, radius (r) = 2.1 cm
When a hemisphere is scooped out from each end, the article exposes:
- Curved Surface Area (CSA) of the cylinder
- CSA of two hemispheres (one from each end)
(The flat circular ends of the cylinder are removed along with the scooping.)
Total Surface Area = CSA of cylinder + 2 × CSA of hemisphere
$$= 2\pi rh + 2 \times 2\pi r^2$$
$$= 2\pi r(h + 2r)$$
$$= 2 \times \frac{22}{7} \times 2.1 \times (5.8 + 2 \times 2.1)$$
$$= 2 \times \frac{22}{7} \times 2.1 \times (5.8 + 4.2)$$
$$= 2 \times \frac{22}{7} \times 2.1 \times 10$$
$$= 2 \times 22 \times 0.3 \times 10$$
$$= 132 \text{ cm}^2$$
∴ Total surface area of the article = 132 cm²
Source: Chapter 12, Section 12.2 — Surface Area of a Combination of Solids
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Explanation
- The key insight: when hemispheres are scooped out from each end, the flat circular ends of the cylinder disappear, but the curved surfaces of the hemispheres are now part of the outer surface. So TSA = CSA of cylinder + 2 × CSA of hemisphere (not TSA of hemisphere, since the flat face is open/removed).
- Examiners award marks for: correct formula, correct substitution, correct simplification, and the final answer with units.
- Note: $2\pi r \times 2r = 4\pi r^2$ represents both hemispheres combined = one full sphere's surface area. Factoring as $2\pi r(h + 2r)$ saves calculation steps.