Question

The spherical shell of lead whose external diameter is 18 cm is melted and recast into a right circular cylinder of height 8 cm and diameter 12cm. determine the internal diameter of the shell

Answer 1

Answer:

Internal diameter of the shell is 16 cm.

Step-by-step explanation:

We know the volume of sphere is 4/3 $\pi r^{3}$ and volume of right circular $\pi r^{2}h$

In the given problem, difference of volume of sphere with external radius and internal radius is equal to volume of right circular cylinder.

Here, the external radius of spherical shell is 9 cm and let the internal radius of the shell is "r".

The radius of right circular cylinder is 6 cm

Hence,

4/3 $\pi9^{3}$ - 4/3 $\pi r^{3}$ = $\pi 6^{2} 8$

On solving the above equation,

we get r = 8 cm (Approx.)

Internal diameter = 2 x 8 = 16 cm