Question

A sphere is melted to form a cylinder whose height is 36 times of its radius. What is the ratio of radii of sphere to the cylinder?
Select an answer
A 3 : 1
B 6 : 1
C 1 : 3
D 1 : 6

Answer 1

A sphere is melted to form a cylinder whose height is 36 times of its radius.

$\frac{4}{3} \pi \times {R}^{3} = \pi \times {r}^{2} h$

For a Cylinder :

$h = 36r$

Then,

$\frac{4}{3} \pi \times {R}^{3} = \pi \times {r}^{2} h \\ \frac{4}{3} \pi \times {R}^{3} = \pi \times {r}^{2} \times 36r \\ \frac{ {R}^{3} }{ {r}^{3} } = \frac{36 \times 3}{4} = \frac{3}{1}$

The correct option is (A) 3 : 1