Question
If a solid sphere of radius 10cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is:
✓
Answer
- $100\pi$
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).
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In figure, if lines l and m are parallel lines, then x =
- 70°
- 100°
- 40°
- 30°
When polynomial $x^2 + 3x^2 + 3x + 1$ is divided by $x + 1,$ the remainder is:
→Write the correct answer in the following: If $x + 1$ is a factor of the polynomial $2x^2 + kx$, then the value of $k$ is.
→Where $p(x) = x^4 + 2x^3 - 3x^2 - 1$ is divided by $(x - 2),$ the remainder is:
→$\frac{1}{\sqrt{9}-\sqrt{8}}$ is equal to :
→Angle inscribed in a semicircle is:
The area of the floor of a room is $15m^2.$ If its height is $4m,$ them the volume of the air contained in the room is:
→If the volume of two cones are in the ratio $1 : 4$ and their diameters are in the ratio $4 : 5,$ then the ratio of their heights, is:
→If $\sqrt2=1.4142,$ then $\sqrt{\frac{\sqrt2-1}{\sqrt2+1}}$ is equal to:
→If $a = 2, b = 3,$ then the value of $(a^b + b^a)^{-1}$ is:
→