Question

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?

Answer 1

Answer:

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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