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

#### 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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