Eight identical spheres of radius r are placed at the vertices of a cube such that each sphere touches its three neighboring spheres. What is the side length of the cube?

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EEJ MAIN Aptitude QUESTION #10994

Question 1

Eight identical spheres of radius $r$ are placed at the vertices of a cube such that each sphere touches its three neighboring spheres. What is the side length of the cube?

$2r$✔️
$2r(1+\sqrt{2})$
$2r(1+\sqrt{3})$
$4r$

Correct Answer Explanation

If spheres at adjacent vertices touch, the distance between centers equals $2r$. For a cube of side $a$, adjacent vertices are distance $a$ apart. Thus $a = 2r$.

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