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Question

Determine the ratio of the length of the longest rod that can be fitted in a sphere to the length of the longest rod that can be fitted in a cube, given that the sphere exactly fits inside the cube.


A

3:1

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B

1:3

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C

1 : 1

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D

2 : 1

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Solution

The correct option is B

1:3


Let the side of the cube be x.
Diameter of sphere = x.
[The sphere fits exactly into the cube]

Length of the longest rod that can be fit into the cube
= main diagonal of the cube across the opposite vertices
=3x

Length of the longest rod that can be fit into a sphere is the diameter i.e. x.

Ratio of length of the longest rod in sphere to the length of the longest rod in cube
=x3x

=13


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