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# In a cube of side 10, what is the length of the line joining the cente

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Director
Joined: 19 Oct 2018
Posts: 697
Location: India
In a cube of side 10, what is the length of the line joining the cente  [#permalink]

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25 May 2019, 19:33
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35% (medium)

Question Stats:

83% (02:17) correct 17% (01:25) wrong based on 18 sessions

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In a cube of side 10, what is the length of the line joining the center of any face and a vertex of the cube not contained in the plane of that face?

A. $$\sqrt{6}$$
B. $$3\sqrt{5}$$
C. $$5\sqrt{3}$$
D. $$5\sqrt{6}$$
E. $$10\sqrt{6}$$
ISB School Moderator
Joined: 08 Dec 2013
Posts: 529
Location: India
Concentration: Nonprofit, Sustainability
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
Re: In a cube of side 10, what is the length of the line joining the cente  [#permalink]

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25 May 2019, 20:48
nick1816 wrote:
In a cube of side 10, what is the length of the line joining the center of any face and a vertex of the cube not contained in the plane of that face?

A. $$\sqrt{6}$$
B. $$3\sqrt{5}$$
C. $$5\sqrt{3}$$
D. $$5\sqrt{6}$$
E. $$10\sqrt{6}$$

Step 1: I drop a perpendicular from the center of the face (A) to the opposite face (B), which is also the center of the opposite face. This length is 10.
Step 2: I draw a st. line from A to the vertex of opposite face (C).

Distance between BC= 1/2 of diagonal of the face containing B
= (1/2) * 10*root(2)
Now Pythagoras theorem to find AC
AC^2 = [5(root 2)]^2 + 10^2

AC= 5 root(6), IMO D
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Re: In a cube of side 10, what is the length of the line joining the cente   [#permalink] 25 May 2019, 20:48
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