Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
If a cylindrical tower $D$ metres in diameter and $H$ metres high is capped with a semi-spherical dome, then the total visible surface of the tower will be
(a)$\frac{\pi D}{2}(2 H+D)$
(b)$\frac{\pi D}{3}(H+2 D)$
(c)$\frac{\pi D}{2}\left(2 H+\frac{D}{2}\right)$
(d)$\frac{\pi D}{3}\left(2 H+\frac{D}{2}\right)$
Answer
Answer (as printed): A
Explanation
Total visible surface area = Curved surface area of cylinder + Curved surface area of hemisphere = $$\begin{aligned} {\left[2 \pi \times \frac{D}{2} \times H+2 \pi \times\left(\frac{D}{2}\right)^{2}\right] \mathrm{m}^{2} } & =\left(\pi D H+\frac{\pi D^{2}}{2}\right) \mathrm{m}^{2} \\ & =\left[\frac{\pi D}{2}(2 H+D)\right] \mathrm{m}^{2} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.