GATE Mechanical 2016 Set 2 | GA | Question: 1

Question

The volume of a sphere of diameter $1$ unit is ________ than the volume of a cube of side $1$ unit.

• A. least
• B. less
• C. lesser
• D. low

Comments

sphere touches the cube side to be as big its side(1 unit).

oh!, the question is for checking English, then "less" is suitable.

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Less is appropriate option

• Less: This is the comparative form of "little" and is used to indicate a smaller amount or degree. It is appropriate for comparing quantities.
• Lesser: This term is often used in more formal or legal contexts, typically to refer to something of lower rank or importance rather than quantity.

Answer 1

'Lesser' and 'than' both are comparative words and using them together is grammatical error. Either say 'Sphere is lesser in volume than Cube for same diameter and edge length' or say 'Sphere is less than........'.

Answer 2

The volume of a sphere of diameter 11 unit is less than the volume of a cube of side 11 unit.
option B..

Answer 3

Never use lesser than for comparing ,

With comparative words( adjective with -er as suffix) generally than is used , but it is not true for the case of less

 Here we will use less than (<)  

Example -

2 is less than 4  OR  2 is lesser than  4

Of course the first one (2 is less than 4 ) is right

Answer 4

Answer B

The volume of the sphere is $\frac{4}{3} * \pi * r^3$ so if diameter is $1$ unit than Radius is 0.5 unit so 

Volume = $ \frac{4}{3} * 3.14 * (0.5)^3$ = 0.5233 $unit^3$

volume of the cube with side 1 unit = $(side)^3 $= $(1)^3 $ = 1 $unit^3$

so the volume of a sphere of diameter 1 unit is less than the volume of a cube of side 1 unit.