Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surfaces will be [SSC-CHSL (10+2) Exam, 2015]
(a)$\sqrt{2}: 1$
(b)$1: \sqrt{2}$
(c)2 : 1
(d)1 : 2
Answer
Answer (as printed): A
Explanation
Let $\mathrm{OP}=\mathrm{OQ}=\mathrm{OR}=r$ $\therefore \mathrm{OR}=h=r$ ∴ Curved surface area of the hemisphere $=2 \pi r^{2}$ Curved surface area of a cone $=\pi r l$ Where $l=\sqrt{h^{2}+r^{2}}=\sqrt{r^{2}+r^{2}}=r \sqrt{2}$ $$\begin{aligned} \therefore \text { Required ratio } & =\frac{2 \pi r^{2}}{\pi r l}=\frac{2 \pi r^{2}}{\pi r \cdot r \sqrt{2}} \\ = & \frac{2}{\sqrt{2}}=\frac{2 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}}=\frac{2 \sqrt{2}}{2}=\frac{\sqrt{2}}{2}=\frac{\sqrt{2}}{1}=\sqrt{2}: 1 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.