In a cube of side 10, what is the length of the line joining the centre of any face and a vertex of the cube not contained in the plane of that face?
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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. √6
B. 3√5
C. 5√3
D. 5√6
E. 10√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
Step-by-step explanation:
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