Question

16 hemispheres of radius 2 cm are melted to make a single sphere. Find the radius of the sphere.

• A. 8 cm
• B. 16 cm
• C. 4 cm
• D. 32 cm

Answer 1

The correct option is C 4 cm

Let the radius of sphere and hemisphere be $r_2$ and $r_1$ respectively.
Volume of one hemisphere = $\frac{2}{3}$ $\times$ $\frac{22}{7}\times r_1^3$
Volume of a sphere = $\frac{4}{3}$ $\times$ $\frac{22}{7}\times r_2^3$
According to the question,
16 $\times$ $\frac{2}{3}$ $\times$ $\frac{22}{7}\times r_1^3$ = $\frac{4}{3}$ $\times$ $\frac{22}{7}\times r_2^3$
$\Rightarrow$​ $r_2^3$ = 8$r_1^3$
$\Rightarrow$ $r_2^3$ = $2^3$​ $\times$ $2^3$​ [$\because$ $r_1$ = 2 cm ]
​$\Rightarrow$ $r_2$ = 2 $\times$ 2
$\Rightarrow$ $r_2$ = 4 cm