Question

If V and S represent respectively the volume & surface area of a cuboid of length l, breadth b and height h. Prove that 1/v=2/s(1/l+1/b+1/h)

Answer 1

SOLUTION

GIVEN

V and S represent respectively the volume & surface area of a cuboid of length l, breadth b and height h.

TO PROVE

$\displaystyle \sf{ \frac{1}{V} = \frac{2}{S} \bigg( \: \frac{1}{l} + \frac{1}{b} + \frac{1}{h} \bigg) }$

EVALUATION

Here it is given that V and S represent respectively the volume & surface area of a cuboid of length l, breadth b and height h.

∴ V = lbh

∴ S = 2( lb + lh + bh )

Now

LHS

$\displaystyle \sf{ = \frac{1}{V} }$

$\displaystyle \sf{ = \frac{1}{lbh} }$

RHS

$\displaystyle \sf{ = \frac{2}{S} \bigg( \: \frac{1}{l} + \frac{1}{b} + \frac{1}{h} \bigg) }$

$\displaystyle \sf{ = \frac{2}{S} \bigg( \: \frac{lb + lh + bh}{lbh} \bigg) }$

$\displaystyle \sf{ = \frac{S}{S} \times \frac{1}{lbh} }$

$\displaystyle \sf{ = \frac{1}{lbh} }$

∴ LHS = RHS

Hence proved

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Answer 2

Step-by-step explanation:

SOLUTION

GIVEN

V and S represent respectively the volume & surface area of a cuboid of length l, breadth b and height h.

TO PROVE

\displaystyle \sf{ \frac{1}{V} = \frac{2}{S} \bigg( \: \frac{1}{l} + \frac{1}{b} + \frac{1}{h} \bigg) }

V

1

=

S

2

(

l

1

+

b

1

+

h

1

)

EVALUATION

Here it is given that V and S represent respectively the volume & surface area of a cuboid of length l, breadth b and height h.

∴ V = lbh

∴ S = 2( lb + lh + bh )

Now

LHS

\displaystyle \sf{ = \frac{1}{V} }=

V

1

\displaystyle \sf{ = \frac{1}{lbh} }=

lbh

1

RHS

\displaystyle \sf{ = \frac{2}{S} \bigg( \: \frac{1}{l} + \frac{1}{b} + \frac{1}{h} \bigg) }=

S

2

(

l

1

+

b

1

+

h

1

)

\displaystyle \sf{ = \frac{2}{S} \bigg( \: \frac{lb + lh + bh}{lbh} \bigg) }=

S

2

(

lbh

lb+lh+bh

)

\displaystyle \sf{ = \frac{S}{S} \times \frac{1}{lbh} }=

S

S

×

lbh

1

\displaystyle \sf{ = \frac{1}{lbh} }=

lbh

1

∴ LHS = RHS

Hence proved

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