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:
- ✓$100\pi$
- B$75\pi$
- C$60\pi$
- D$50\pi$
✓
Answer
Correct option: A.
$100\pi$
Volume of solid sphere $=\frac{4}{3}\pi(10)^3=\frac{4000\pi}{3}\text{ cm}^3$
Vomule $8$ solid sphere of radius $($say$)\ \text{r}=8\times\frac{4}{3}\pi\text{r}^3=\frac{32\pi\text{r}^3}{3}\text{ cm}^3$
Now, $\frac{32\pi\text{r}^3}{3}=\frac{4000\pi}{3}$
$\Rightarrow\text{r}=\Big(\frac{1000}{8}\Big)^\frac{1}{3}$
$=\frac{10}{2}=5\text{ cm}$
Surface Area of each small ball $=4\pi\text{r}^2$
$=4\pi(5)^2=100\pi\text{ cm}^2 $
Hence, correct option is $(a)$.
Vomule $8$ solid sphere of radius $($say$)\ \text{r}=8\times\frac{4}{3}\pi\text{r}^3=\frac{32\pi\text{r}^3}{3}\text{ cm}^3$
Now, $\frac{32\pi\text{r}^3}{3}=\frac{4000\pi}{3}$
$\Rightarrow\text{r}=\Big(\frac{1000}{8}\Big)^\frac{1}{3}$
$=\frac{10}{2}=5\text{ cm}$
Surface Area of each small ball $=4\pi\text{r}^2$
$=4\pi(5)^2=100\pi\text{ cm}^2 $
Hence, correct option is $(a)$.
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