A hollow copper pipe of inner diameter 6 cm and outer diameter 10 cm is melted and changed into a solid circular cylinder of the same height as that of the pipe. Find the diameter of the solid cylinder.

Given,

Internal radius (r) = $\dfrac{6}{2}$ = 3 cm.

Outer radius (R) = $\dfrac{10}{2}$ = 5 cm.

Given, height of the old hollow and new solid cylinder is equal let it be h.

Let the radius of new solid cylinder be r₁.

Since, old hollow cylinder is recasted into solid cylinder hence, their volume will be equal.

$\therefore π(R^2 - r^2)h = πr_1^2h$

Dividing both sides by π and h,

$\Rightarrow R^2 - r^2 = r$1^2 \\[1em] \Rightarrow r1^2 = 5^2 - 3^2 \\[1em] \Rightarrow r1^2 = 25 - 9 \\[1em] \Rightarrow r1^2 = 16 \\[1em] \Rightarrow r_1 = 4 \text{ cm}.

Diameter = 2 × Radius = 2 × 4 = 8 cm.

Hence, the diameter of solid cylinder = 8 cm.