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
(a)1 : 2
(b)2 : 1
(c)$1: \sqrt{2}$
(d)$\sqrt{2}: 1$
Answer
Answer (as printed): D
Explanation
Let the radius of each be $R$. Height of hemisphere, $H=R$. So, height of cone = height of hemisphere = R. Slant height of cone $=\sqrt{R^{2}+R^{2}}=\sqrt{2} R$. $\frac{\text { Curved surface area of hemisphere }}{\text { Curved surface area of cone }}=\frac{2 \pi R^{2}}{\pi R \times \sqrt{2} R}=\sqrt{2}: 1$.
Explanation as extracted from the printed page; notation may be imperfect.