Question

A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be

Options

• 4

• 3

• 6

• 8

Answer 1

In the given problem, we have a cylindrical rod of the given dimensions:

Radius of the base (r_c) = x units

Height of the cylinder (h) = 8x units

So, the volume of the cylinder (V_c) =  ` pi r^2 h`

`= pi x^2 (8x) `

`= 8 pi x^3`

Now, this cylinder is remolded into spherical balls of same radius. So let us take the number of balls be y.

Total volume of y spheres (V_s) = `y(4/3 pi r^3) `

=`y(4/3 pi x^3)`

So, the volume of the cylinder will be equal to the total volume of y number of balls.

We get,  `V_c = yV_s`

`8 pi x^3 = y (4/3 pi x^3)`

        ` 8 = 4/3 y`

        ` y = ((8)(3))/4`

          y = 6

Therefore, the number of balls that will be made is 6 .