Question

If the world is a perfect sphere of radius 6371 km, then what would the side length of the biggest cube that can fit inside it be?
$(Take\sqrt{3}=\frac{6371}{3671})$

• A. 6371 km
• B. 7342 km
• C. 6342 km
• D. 7371 km

Answer 1

The correct option is B 7342 km

$\text{Length of the diagonal of a cube of}\text{sidelength 'a'}=\sqrt{3}\times a$

Now, picturing the diagonal of the largest cube that can fit in the sphere, we find:


Hence, the diagonal of the cube also forms the diameter of the sphere.

$⟹\sqrt{3}\times a=2\times radiusofthesphere$
$⟹\frac{6371}{3671}\times a=2\times 6371km$
$⟹a=2\times 3671km$
$⟹a=7342km$

Therefore, the side length of the largest cube that can fit inside a perfectly spherical Earth is 7342 km.