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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


Team Careers360 20th Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

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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