Vincen wrote:If the length of the largest straight rod that can be put inside a cuboid is 10 m, then the surface area of the cuboid cannot be more than
A) 100 m^2
B) 200 m^2
C) 400 m^2
D) 600 m^2
E) Cannot be determined
The OA is B.
I couldn't determine it. Someone help me.
The length of the largest straight rod that can be put inside a cuboid equals to the longest diagonal of the cuboid.
Say the sides of the cuboid are a, b, and c meters.
Thus, the longest diagonal = √(a^2 + b^2 + c^2)
=> √(a^2 + b^2 + c^2) = 10
a^2 + b^2 + c^2 = 100
If all the sides of the cuboid are equal, then a = b = c.
Thus, 3a^2 = 100
We know that the surface area of the cube = 6a^2
Thus, the surface area of the cube = 6a^2 = 2*100 = 200 meter^2
200 m^2 is the maximum possible surface area of a cuboid.
The correct answer:
B
Hope this helps!
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