An insect wants to go from one corner of cube to diagonaly opposite corner by crawling [can't fly]. Minimum distance it has to travel to reach there if side of cube is a

\sqrt{3} a

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a + \sqrt{2} a

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3 a

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\sqrt{5} a

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Solution

The correct option is D $\sqrt{5} a$

Path for D to F is = DI + IF
Say the distance AI = $x$
The total path length, $L = \sqrt{a^{2} + x^{2}} + \sqrt{(a - x)^{2} + a^{2}}$
By maxima or minima $\frac{d L}{d x} = 0 \Rightarrow x = \frac{a}{2}$
So $L = \sqrt{5} a$
DI is in the ABCD plane & IF is in the ABFE plane.

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An insect wants to go from one corner of cube to diagonaly opposite corner by crawling [can't fly]. Minimum distance it has to travel to reach there if side of cube is a

The correct option is D √5a Path for D to F is = DI + IF Say the distance AI = x The total path length, L=√a2+x2+√(a−x)2+a2 By maxima or minima dLdx=0⇒x=a2 So L=√5a DI is in the ABCD plane & IF is in the ABFE plane.