Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2007 · Marks: · Difficulty:
A solid metallic right circular cylinder of base diameter 16 cm and height 2 cm is melted and recast into a right circular cone of height three times that of the cylinder. Find the curved surface area of the cone. [Use $\pi=3.14$ ]
(a)$196.8 \mathrm{cm}^{2}$
(b)$228.4 \mathrm{cm}^{2}$
(c)$251.2 \mathrm{cm}^{2}$
(d)None of these
Answer
Answer (as printed): C
Explanation
Let the radius of the cone be $r \mathrm{cm}$. Then, $\pi \times 8^{2} \times 2=\frac{1}{3} \times \pi \times r^{2} \times 6 \Rightarrow r=8$. Slant height, $l=\sqrt{r^{2}+h^{2}}=\sqrt{8^{2}+6^{2}}=\sqrt{100} \mathrm{cm}=10 \mathrm{cm}$. Curved surface area of cone $=\pi r l=(3.14 \times 8 \times 10) \mathrm{cm}^{2}$ $$=251.2 \mathrm{cm}^{2}$$