Question

The radii of the internal and external surfaces of a metallic spherical shell are $3\text{cm}$ and $5\text{cm}$ respectively. It is melted and recast into a solid right circular cylinder of height $10.67\text{cm}$. Then, the diameter of the base of the cylinder is approximately:

• A. $5\text{cm}$
• B. $6\text{cm}$
• C. $7\text{cm}$
• D. $8\text{cm}$

Answer 1

The correct option is C $7\text{cm}$

Volume of cylinder = Volume of spherical shell
$\pi r^{2}h=\left(4/3\right)\pi (R_1^3-R_2^3)$
$\Rightarrow r^2\left(10.67\right)=\left(\frac{4}{3}\right)(125-27)$
$\Rightarrow r^2=\left(\frac{4}{3}\right)\left(\frac{98}{10.67}\right)\sim 12.25$
$\Rightarrow r\sim 3.5\text{cm}$
$\Rightarrow d\sim 7\text{cm}$