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Mathematics — CBSE Class 10 board question

Q1. [1]
The total surface area of a solid hemisphere whose diameter is $d$ is:
  1. (a) $3\pi d^2$
  2. (b) $2\pi d^2$
  3. (c) $\frac{1}{2}\pi d^2$
  4. (d) $\frac{3}{4}\pi d^2$
Previously asked in CBSE board exam
2023 30/2/1 Q10
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer

(d) $\dfrac{3}{4}\pi d^2$

Since radius $r = \dfrac{d}{2}$, TSA of solid hemisphere $= 3\pi r^2 = 3\pi \left(\dfrac{d}{2}\right)^2 = \dfrac{3}{4}\pi d^2$.

Explanation

TSA of a solid hemisphere = curved surface area + circular base = $2\pi r^2 + \pi r^2 = 3\pi r^2$. Substituting $r = d/2$ gives $\frac{3}{4}\pi d^2$. Students often forget to include the flat circular base, which leads to the wrong option (b).

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