Question

The number of solid spheres, each of diametres 6 cm, that could be moulded to form a solid metal cylinder of height 45 cm and diameter 4 cm is

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (C)

5

Number of spheres made $=\frac{Volumeofcylinder}{Volumeofeachspherel}$
Volume of a Cylinder of Radius "R" and height "h" $ = \pi { R }^{ 2 }h $

Volume of a sphere of radius 'r' $=\frac{4}{3}\pi r^3$
As the diameter of the ball is $6$ cm, its radius r $=3$ cm

Radius of the cylinder $=2cm$
Hence, number of balls made $=\frac{\pi \times 2^2\times 45}{\frac{4}{3}\pi \times 3^3}=5$