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Mathematics — CBSE Class 10 board question

Q1. [1]
A camping tent in hemispherical shape of radius 1.4 m, has a door opening of area 0.50 m$^2$. Outer surface area of the tent is
  1. (A) $11.78$ m$^2$
  2. (B) $12.32$ m$^2$
  3. (C) $11.82$ m$^2$
  4. (D) $12.86$ m$^2$
Previously asked in CBSE board exam
2026 30/5/1 Q12
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer

(A) 11.78 m²

CSA of hemisphere = $2\pi r^2 = 2 \times \dfrac{22}{7} \times 1.4 \times 1.4 = 12.32 \text{ m}^2$

Outer surface area = $12.32 - 0.50 = \mathbf{11.82}$ — wait:

$2 \times \frac{22}{7} \times 1.96 = 12.32\ \text{m}^2$; subtracting door area: $12.32 - 0.50 = 11.82\ \text{m}^2$

(C) 11.82 m²

Explanation

The tent is hemispherical, so its curved surface area = $2\pi r^2 = 2 \times \frac{22}{7} \times (1.4)^2 = 12.32\ \text{m}^2$. The door opening (0.50 m²) is cut out from this surface, so outer surface area = $12.32 - 0.50 = 11.82\ \text{m}^2$. Key point: subtract only the door area, not the base (hemispherical tent has no floor canvas).

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