Question : The radius of a large solid sphere is 14 cm. It is melted to form 8 equal small solid spheres. What is the sum of the total surface areas of all 8 small solid spheres? (use $\pi=\frac{22}{7}$)
Option 1: 3648 cm2
Option 2: 4928 cm2
Option 3: 4244 cm2
Option 4: 4158 cm2
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Correct Answer: 4928 cm 2
Solution :
Given: The radius of a large solid sphere is 14 cm.
The volume of the sphere of radius $r$ is $\frac{4}{3}\times \frac{22}{7}\times r^3$. Its total surface area is $4\times \frac{22}{7}\times r^2$.
The volume of a large solid sphere is $\frac{4}{3}\times \frac{22}{7}\times (14)^3=11499$ cm
3
.
It is melted to form 8 equal small solid spheres $=\frac{11499}{8}=1437.4$ cm
3
.
The volume of one sphere is 1437.4 cm
3
.
$\frac{4}{3}\times \frac{22}{7}\times r^3=1437.4$
⇒ $r^3=343$
⇒ $r=7$ cm
The sum of the total surface areas of all 8 small solid spheres $8 × 4\times \frac{22}{7}\times 7^2=4928$ cm
2
.
Hence, the correct answer is 4928 cm
2
.
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