Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A cylindrical rod of iron whose height is eight times its radius is melted and cast into spherical balls each of half the radius of the cylinder. The number of spherical balls is
(a)12
(b)16
(c)24
(d)48
Answer
Answer (as printed): D
Explanation
Let the radius of the cylindrical rod be $r$. Then, height of the $\operatorname{rod}=8 r$ and radius of one ball $=\frac{r}{2}$. $$\text { ∴ Number of balls }=\frac{\pi \times r^{2} \times 8 r}{\frac{4}{3} \pi \times\left(\frac{r}{2}\right)^{3}}=\left(\frac{8 \times 8 \times 3}{4}\right)=48 .$$
Explanation as extracted from the printed page; notation may be imperfect.