Question

A solid cylinder of iron whose diameter is 18 cm and height 12 cm is melted and turned into a solid sphere. Find the diameter of the sphere so formed​

Answer 1

Answer:

Diameter of sphere = 18 cm

Step-by-step explanation:

Volume of Cylinder and Sphere:

Cylinder:

     Diameter = 18 cm

                  r = 18÷ 2 = 9 cm

                 h = 12 cm

$\sf \boxed{\bf Volume \ of \ cylinder = \pi r^2h}$

                                    = π * 9 * 9 * 12 cm³

Sphere:

  $\sf \boxed{\text{\bf Volume of sphere = \dfrac{4}{3} \pi r^3 }}$

Solid cylinder is melted and turned into a solid sphere.

Volume of sphere = volume of cylinder

 $\sf \dfrac{4}{3}\pi r^3 = \pi *9*9*12$

      $\sf r^{3}= \dfrac{\pi *9*9*12*3}{4*\pi }\\\\ r^{3}=9 * 9 *3 *3\\\\\\r = \sqrt[3]{9*9*9}\\\\ r = 9 \ cm\\\\diameter = 9*2\\\\\boxed{diameter \ of \ sphere = 18 \ cm}$