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

Diameter of sphere = 18 cm

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 = $(4)/(3) \pi r^3$}}`

Solid cylinder is melted and turned into a solid sphere.

Volume of sphere = volume of cylinder

`\sf (4)/(3)\pi r^3 = \pi *9*9*12`

`\sf r^(3)= (\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}`