Question

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

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

Answer 1

Answer: (C)

$2cm$

Volume of the cylinder, $V_c=\pi r^{2}h$

Volume of the cylinder, $V_c=12\times V_s$ ($V_s$ is volume of the sphere)

$\pi r_c^{2}h=12\times \frac{4}{3}\pi r_s^3$

$\pi \times 1^2\times 16=12\times \frac{4}{3}\pi r_s^3$

$r_s=1cm$

So, diameter of each sphere is $2cm$.

Hence, option C.