MCQ
If a solid sphere of radius $10\ cm$ is moulded into $8$ spherical solid balls of equal radius, then the surface area of each ball (in sq. cm) is:
- A$60\pi$
- ✓$100\pi$
- C$50\pi$
- D$75\pi$
✓
Answer
Correct option: B.
$100\pi$
Volume of sphere $=\big(\frac{4}{3}\big)\pi\text{r}^3$
Given, solid sphere of radius $10\ cm$ is moulded into $8$ spherical solid balls of equal radius
$=\big(\frac{4}{3}\big)\pi\times10^3=8\times\big(\frac{4}{3}\big)\pi\text{r}^3$
$\Rightarrow\text{r}=\frac{10}{2}=5\text{m}$
Surface area of a sphere $=4\pi\text{r}^2$
Thus, the surface area of each sphere $=4\times\pi\times5^2=100\pi$
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