Question : The length of the largest possible rod that can be placed in a cubical room is $35\sqrt3$ metre. The surface area of the largest possible sphere that fits within the cubical room (assuming $\pi=\frac{22}{7}$) (in sq. metres) is:
Option 1: 3,500
Option 2: 3,850
Option 3: 2,450
Option 4: 4,250
Correct Answer: 3,850
Solution :
Given: The length of the largest possible rod that can be placed in a cubical room is $35\sqrt3$ metres.
The length of the largest rod = diagonal of the cube = side × $\sqrt3$
Here, side × $\sqrt3=35\sqrt3$
Or, the side of the cube = 35 metres
Now, the radius of the largest possible sphere that fits within the cubical room = $\frac{35}{2}$ metres
Therefore, the surface area of the sphere:
= $4\pi (\frac{35}{2})^2$
= $4×\frac{22}{7}×\frac{35}{2}×\frac{35}{2}$
= 3850 sq. metres
Hence, the correct answer is 3850.
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