Question

The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 28 cm. Find the length of the wire.

Answer 1

since the sphere is melted and converted into a cylindrical wire, the volume of the sphere is the same as that of the cylinder.

The volume of a sphere is

$V=\frac{4}{3}\pi r^3$ where r is its radius.

The volume of a cylinder is

$V=\pi r^{2}h$ where r is its radius and h is its height.

Diameter of sphere is 42 cm.

Thus, for the sphere radius r is 21 cm.

Diameter of cylinder is 28 cm.

Thus, for the cylinder radius r is 14 cm.

Thus, volume of sphere is

$V_1=\frac{4}{3}\pi (21{)}^3$

Thus, volume of cylinder is

$V_2=\pi (14{)}^{2}h$

$V_1=V_2\frac{4}{3}\pi (21{)}^3=\pi (14{)}^{2}h\frac{4\times (21{)}^3}{3}=(14{)}^{2}hh=\frac{4\times (21{)}^3}{3\times (14{)}^2}=\frac{4\times 9261}{3\times 196}=\frac{37044}{588}=63cm$

height of cylinder = 63 cm