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) plz send the answer on paper I really want
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Answered by
2
a , b , c are dimensions of the
cuboid.
S = 2 ( ab + bc + ca )
V = abc
RHS = 2/S(1/a + 1/b + 1/c )
= 2/[ 2( ab+bc+ca )] { 1/a+ 1/b + 1/c}
= 1/( ab+ bc +ca ) {( bc + ac + ab )/abc }
= 1/abc
= 1/V
= LHS
Hope it helps
:)
Answered by
2
Given that
Length = a
Breadth = b
Height = c
Volume (v) = l x b x h
= a x b x c = abc
Surface area = 2(lb + bh + hl)
= 2(ab + bc + ac)
Now,
2/5 ( 1/a +1/b + 1/c )
2/2(ab+bc+ac) (ab +bc + ca)/ abc
1/abc= 1/V
HENCE PROVED//
Length = a
Breadth = b
Height = c
Volume (v) = l x b x h
= a x b x c = abc
Surface area = 2(lb + bh + hl)
= 2(ab + bc + ac)
Now,
2/5 ( 1/a +1/b + 1/c )
2/2(ab+bc+ac) (ab +bc + ca)/ abc
1/abc= 1/V
HENCE PROVED//
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