Q1. [1] § 12.2 Surface Area of a Combination of Solids § 12.4 Summary
The total surface area of a solid hemisphere of diameter '$2d$' is :
- (a) $3\pi d^2$
- (b) $2\pi d^2$
- (c) $\frac{1}{2}\pi d^2$
- (d) $\frac{3}{4}\pi d^2$
Previously asked in CBSE board exam
2026 30/1/1 Q16
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer
(a) $3\pi d^2$
Diameter = $2d$, so radius $r = d$.
TSA of solid hemisphere $= 2\pi r^2 + \pi r^2 = 3\pi r^2 = 3\pi d^2$.
Explanation
TSA of a solid hemisphere = curved surface area ($2\pi r^2$) + circular base area ($\pi r^2$) = $3\pi r^2$. Here $r = d$, so the answer is $3\pi d^2$. Don't forget the flat circular base — a common mistake.
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