Question

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is

• A. 4 cm
• B. 3 cm
• C. 2 cm
• D. 6 cm

Answer 1

Answer: (C)

2 cm

Volume of a sphere of radius 'r' $=\frac{4}{3}\pi r^3$
Volume of a Cylinder of Radius "R" and height "h" $=\pi R^{2}h$
As the diameter of the cylinder is $2$ cm, its radius r $=1$ cm
Now, Volume of $12$ spheres $=$ Volume of the cylinder.
$12\times \frac{4}{3}\pi r^3=\pi \times 1^2\times 16$
$r^3=1$
$r=1cm$
Hence, diameter of the sphere $=2cm$