Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A solid cylinder and a solid cone have equal base and equal height. If the radius and height be in the ratio of $4: 3$, the ratio of the total surface area of the cylinder to that of the cone is
(a)10 : 9
(b)11 : 9
(c)12 : 9
(d)14 : 9
Answer
Answer (as printed): D
Explanation
Let the radius and height of the cone and the cylinder be $4 x$ and $3 x$ respectively. Then, total surface area of cylinder $=[2 \pi(4 x)(4 x+3 x)]$ sq. units $=(8 \pi x .7 x)$ sq. units. $=\left(56 \pi x^{2}\right)$ sq. units. Slant height of cone, $l=\sqrt{(4 x)^{2}+(3 x)^{2}}=\sqrt{25 x^{2}}=5 x$. Total surface area of cone $=\pi r(l+r)=\pi .4 x(5 x+4 x)$ $=\left(36 \pi x^{2}\right)$ sq. units $$\text { ∴ } \text { Required ratio }=\frac{56 \pi x^{2}}{36 \pi x^{2}}=14: 9 .$$
Explanation as extracted from the printed page; notation may be imperfect.