XAT 2012 — QA & DI Question 7
Answer the following question based on the information given below.
The following graphs shows the revenue (in $ million) of three companies in their initial six years of operations, in an economy which is characterized by a persistent inflation.
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Ram, a farmer, managed to grow shaped-watermelons inside glass cases of different shapes. The shapes he used were: a perfect cube, hemi-spherical, cuboid, cylindrical along with the normal spherical shaped watermelons. Thickness of the skin was same for all the shapes. Each of the glass cases was so designed that the total volume and the weight of the all the water-melons would be equal irrespective of the shape.
A customer wants to but water-melons for making juice, for which the skin of the water-melon has to be peeled off, and therefore is a waste. Which shape should the customer buy?
Answer & solution
- A
Cube
- B
Hemi-sphere
- C
Cuboid
- D
Cylinder
Normal spherical
Let V be the volume of water-melon, S be the total surface area and t be the thickness of the skin, then volume useable for Juice is, V – St
Hence, if total surface area is minimum, then useable volume of the water-melon will be highest.
Now, for equal volume, sphere has the least surface area.
Hence, option (e).