# CAT Practice : Mensuration

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This is one of the questions which looks difficult on first look but with a little visualization and concept, can be cracked in a minute. This kind of question is more likely to appear in CAT.

## Spheres and Cubes

Q.10: A spherical shaped sweet is placed inside a cube of side 5 cm such that the sweet just fits the cube. A fly is sitting on one of the vertices of the cube. What is the shortest distance the fly must travel to reach the sweet?
1. 2.5 cm
2. 5(√3 – 1) cm
3. 5(√2 – 1) cm
4. 2.5(√3 – 1) cm

Choice D. 2.5(√3 – 1) cm

## Detailed Solution

Diagram :

The question demands visualization. The shortest distance required to be travelled by the fly would be diagonally and be given by:-

Distance = ${\frac{(Diagonal of cube – Diameter of sphere)}{2} }$

= ${\frac{(5√3-5)}{2} }$(Since diagonal of the cube is given as √3 x l)

= ${\frac{5(√3 – 1)/}{2} }$

= 2.5(√3 – 1)

Choice (D) is therefore, the correct answer.

Correct Answer: 2.5(√3 – 1) cm

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## More questions from Mensuration

Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.