Question

What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm ?

Answer 1

Let us take number of solid metallic sphere be x
voluime of sphere = volume of cylinder
4/3 r3 = r^2h
Height of the cylinder melt = 45 cm
Diameter of the cylinder = 12 cm
Radius = 6 cm
Diameter of the sphere = 6 cm
Radius = 3 cm
Volume of the cylinder = $\frac{22}{7}$x 6 x 6 x 45

Volume of each sphere = $\frac{4}{3}\times \frac{22}{7}$x 3 x 3 x 3
Let the number of spheres be 'n'

Volume of all the spheres = Volume of the cylinder

n x$\frac{4}{3}\times \frac{22}{7}$x 3 x 3 x 3 = $\frac{22}{7}$x 6 x 6 x 45
n x $\frac{4}{3}$ x 3 = 45*4
n = 45