Question

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted to form a solid cylinder of base diameter 8 cm. The height of the cylinder is approximate:

• A. 4.5 cm
• B. 4.57 cm
• C. 4.67 cm
• D. 4.7 cm

Answer 1

The correct option is C 4.67 cm

$Volumeofsphere=\frac{4}{3}\pi r^3$
$Volumeofcylinder=\pi r^{2}h$
$Volumeofhollowsphere=\frac{4}{3}\pi ({r_1}^3-{r_2}^3)$
$=\frac{4}{3}\pi (4^3-2^3)$
$=\frac{4}{3}\pi (64-8)$
$=\frac{4}{3}\pi \times 56$
$=\frac{224}{3}\pi$
$Volumeofcylinder=\pi (4{)}^{2}h=16\pi h$
$Volumeofcylinder=Volumeofhollowsphere$
$\Rightarrow \frac{224\pi }{3}=16\pi h$
$\Rightarrow h=\frac{224\pi }{3}\times \frac{1}{16\pi }$
$=\frac{14}{3}$
$\therefore h=4.67cm$