Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, then the ratio of the total surface area of the cylinder to that of the cone is
(a)3 : 1
(b)13 : 9
(c)17 : 9
(d)34 : 9
Answer
Answer (as printed): C
Explanation
Let their radius and height be $5 x$ and $12 x$ respectively. Slant height of the cone, $l=\sqrt{(5 x)^{2}+(12 x)^{2}}=13 x$. $\frac{\text { Total surface area of cylinder }}{\text { Total surface area of cone }}=\frac{2 \pi r(h+r)}{\pi r(l+r)}=\frac{2(h+r)}{(l+r)}$ $$=\frac{2 \times(12 x+5 x)}{(13 x+5 x)}=\frac{34 x}{18 x}=\frac{17}{9} .$$
Explanation as extracted from the printed page; notation may be imperfect.