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) $\frac{3}{4}\pi d^2$

Checks careful reading of the given quantity '$2d$' as the diameter, not the radius.

Concept

• Total surface area of a solid hemisphere of radius r is $\text{TSA} = 3\pi r^2$ (curved surface $2\pi r^2$ + flat base πr²).

Key points

• Diameter = $2d$ ⟹ radius $r = d$.
• Substituting: $\text{TSA} = 3\pi (d)^2 = 3\pi d^2$.

Common mistakes

• Misreading '$2d$' and taking the radius itself as $2d$ instead of the diameter, leading to wrong distractors like 2πd² or (3/4)πd².
• Forgetting to add the base circle's area (πr²) to the curved surface area ($2\pi r^2$).

Real-world

• Used to compute the material needed to manufacture solid hemispherical objects such as bowls, domes, and hemispherical ends of storage tanks and silos.