Question

The diameters of external and internal surfaces of a hollow spherical shell are 10 cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of $2\frac{2}{3}cm$, find the diameter of the cylinder in cm

• A. $14$
• B. $16$
• C. $18$
• D. $20$

Answer 1

The correct option is A $14$

Let the radius of base of the cylinder be 'r'cm. So, Volume of meltallic solid cylinder of height $2\frac{2}{3}cm\left(\frac{8}{3}cm\right)=$ Volume of metal in the spherical shell

$\pi r^2\times \frac{8}{3}=\frac{4}{3}\pi (5^3-3^3)$

$r^2=\frac{4}{3}\times \frac{3}{8}\left(98\right)$

$r^2=49\Rightarrow r=7cm$

Hence, diameter of the cylinder $=14cm$.