Question

One solid hemisphere melted into solid sphere, then what is the ratio of radius of solid sphere hemisphere ?

• A. $\sqrt[3]{32}$ : 1
• B. 8 : 1
• C. 1 : $\sqrt[3]{32}$
• D. 1 : 8

Answer 1

Answer: (C)

1 : $\sqrt[3]{32}$

Let the radius of solid hemisphere be r .

Volume= $\frac{2\pi r^3}{3}$

Hemisphere melted into solid sphere of radius r' (say)

Volume= $\frac{4\pi r^{\prime 3}}{3}$

Now $\frac{2\pi r^3}{3}$=$\frac{4\pi r^{\prime 3}}{3}$

ratio of radius of solid sphere (r') hemisphere (r)

so $\frac{r^{\prime }}{r}=\frac{1}{2^{\frac{1}{3}}}$

Option C.