Question

A solid iron cylinder of radius 4cm and height 18 cms is melted and recast into a sphere what is the radius ofthe sphere

Answer 1

Let y and h be the radius and height of the cylinder respectively.
Let x be the radius of the sphere.

Volume will stay equal.
Volume of sphere = Volume of Cylinder
$\frac{4}{3} \times \pi \times {x}^{3 } = 2\pi \: y\: h$
$4 \times {x}^{3} = 2 \times 4 \times 18 \times 3$
${x}^{3} = \frac{432}{4}$
$x = \sqrt[3]{108}$
x = 4.76 cm
Therefore, radius of sphere will be 4.76 cm