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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