prove that s/2v = 1/l+1/b+1/h, where l,b and h are the length, breadth and height of cuboid and s and v are the surface area and volume respectively.
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Step-by-step explanation:
The dimensions of the cuboid are a,b,c.
We know that, Volume of the cuboid V=abc and surface area of the cuboid S=2(ab+bc+ac)
To prove:
V
1
=
S
2
[
a
1
+
b
1
+
c
1
]
Consider LHS,
V
1
=
abc
1
...(1)
Consider RHS.
S
2
[
a
1
+
b
1
+
c
1
]=
2(ab+bc+ac)
2
[
a
1
+
b
1
+
c
1
]
=
ab+bc+ac
1
[
a
1
+
b
1
+
c
1
]
=
ab+bc+ac
1
[
abc
ab+bc+ac
]
=
abc
1
S
2
[
a
1
+
b
1
+
c
1
]=
abc
1
...(2)
Hence from (1) and (2) we get
V
1
=
S
2
[
a
1
+
b
1
+
c
1
]
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