SSC (English Medium) Class 10th Board ExamMaharashtra State Board
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If ‘V’ is the Volume of a Cuboid of Dimensions a × B × C and ‘S’ is Its Surface Area, Then Prove That: `1/V = 2/S[1/A +1/B + 1/C]` - SSC (English Medium) Class 10th Board Exam - Geometry

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Question

If ‘V’ is the volume of a cuboid of dimensions a × b × c and ‘S’ is its surface area, then prove that: `1/V = 2/S[1/a +1/b + 1/c]`

Solution

The volume (V) of a cuboid = a x b x c

`:. 1/V = 1/(abc)` .......(1)

The surface area (S) of a cuboid = 2(ab + bc + ca)      .....(2)

RHS = `2/S (1/a +  1/b + 1/c)`

`= 2/S ((ab +bc+ac)/(abc))`

`= (2(ab +bc + ca))/(S(abc))`

`= S/(S(abc))`    .......[From (2)]

`= 1/(abc) = 1/V`   ..........[From (1)]

`:. 1/V = 2/S(1/a+ 1/b + 1/c)`

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Solution If ‘V’ is the Volume of a Cuboid of Dimensions a × B × C and ‘S’ is Its Surface Area, Then Prove That: `1/V = 2/S[1/A +1/B + 1/C]` Concept: Surface Area of a Combination of Solids.
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