Question

the ratio of the radii of two sphere is 1:2. the two spheres are melted together to form a cylinder of height which is 12 times its radius. what is the ratio of radius is smaller sphere and the cylinder.? ​

Answer 1

let the radius of smaller sphere be (r1)= x

therefore, radius of bigger sphere (r2)=2x

let the radius of cylinder be = t

let height of cylinder be = h

acc. to ques.

h=12t

as the two spheres are melted to form a cylinder,

hence,

sum of volumes of two spheres = volume of cylinder

$\frac{4}{3} \pi( {(r1)}^{3} + ( {r2})^{3} ) = \pi {t}^{2} h$

$\frac{4}{3} \pi( {x}^{3} + 8 {x}^{3} ) = \pi {t}^{2} (12t) \\ 12\pi {x}^{3} = 12\pi {t}^{3} \\ x = t \\ therefore \\ \frac{x}{t} = 1$