If V be the volume and S be the surface area of a cuboid with dimensio

1.	If V be the volume and S be the surface area of a cuboid with dimensions a × b × c, then which of the following is true?1. \(\frac{1}{V} = \frac{2}{S}\left( {\frac{1}{a} + \frac{1}{b} + \frac{1}{c}} \right)\)2. \(\frac{1}{V} = \frac{2}{S}\left( {a + b + c} \right)\)3. \(\frac{1}{S} = \frac{2}{V}\left( {\frac{1}{a} + \frac{1}{b} + \frac{1}{c}} \right)\)4. None of the above
Answer» Correct Answer - Option 1 : \(\frac{1}{V} = \frac{2}{S}\left( {\frac{1}{a} + \frac{1}{b} + \frac{1}{c}} \right)\) Given Dimensions of cuboid = a × b × c Volume of cuboid = V Surface area of cuboid = S Formula used For a cuboid with length, breadth and height x, y and z respectively, volume = xyz and surface area = 2xy + 2xz + 2yz Calculation V = abc S = 2(ab + bc + ca) On dividing S by V we get, \({S \over V} = {2(ab + bc + ca) \over abc}\) \(\Rightarrow {S \over V} = 2( {ab \over abc}+ {bc \over abc} + {ca \over abc})\) \(\Rightarrow {S \over V} = 2( {1 \over c}+ {1 \over a} + {1 \over b})\) \(\Rightarrow {1 \over V} = {2\over S}( {1 \over a}+ {1 \over b} + {1 \over c})\)

If V be the volume and S be the surface area of a cuboid with dimensions a × b × c, then which of the following is true?1. \(\frac{1}{V} = \frac{2}{S}\left( {\frac{1}{a} + \frac{1}{b} + \frac{1}{c}} \right)\)2. \(\frac{1}{V} = \frac{2}{S}\left( {a + b + c} \right)\)3. \(\frac{1}{S} = \frac{2}{V}\left( {\frac{1}{a} + \frac{1}{b} + \frac{1}{c}} \right)\)4. None of the above

Answer» Correct Answer - Option 1 : \(\frac{1}{V} = \frac{2}{S}\left( {\frac{1}{a} + \frac{1}{b} + \frac{1}{c}} \right)\)

Given

Dimensions of cuboid = a × b × c

Volume of cuboid = V

Surface area of cuboid = S

Formula used

For a cuboid with length, breadth and height x, y and z respectively, volume = xyz and surface area = 2xy + 2xz + 2yz

Calculation

V = abc

S = 2(ab + bc + ca)

On dividing S by V we get,

\({S \over V} = {2(ab + bc + ca) \over abc}\)

\(\Rightarrow {S \over V} = 2( {ab \over abc}+ {bc \over abc} + {ca \over abc})\)

\(\Rightarrow {S \over V} = 2( {1 \over c}+ {1 \over a} + {1 \over b})\)

\(\Rightarrow {1 \over V} = {2\over S}( {1 \over a}+ {1 \over b} + {1 \over c})\)