if l,b,h,s and v are length,breath,height,surface area and volume respectively of a cuboid prove that 1/v=2/s(1/l+1/b+1/h)
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here s = 2 (lb+lh+bh)
s/2 = (lb+lh+bh )---(1)
1/l +1/b +1/h = [ bh+lh+lb]/lbh =(s/2) /lbh = ---(2)
RHS = 2/s * [ 1/l +1/b+1/h]
= 2/s * [(s/2)/lbh] { ∵ (2)}
= 1/ (lbh)
= 1/v [ ∵ volume =v = lbh]
= lhs
s/2 = (lb+lh+bh )---(1)
1/l +1/b +1/h = [ bh+lh+lb]/lbh =(s/2) /lbh = ---(2)
RHS = 2/s * [ 1/l +1/b+1/h]
= 2/s * [(s/2)/lbh] { ∵ (2)}
= 1/ (lbh)
= 1/v [ ∵ volume =v = lbh]
= lhs
knishkabohraknishka:
1/l +1/b +1/h = [ bh+lh+lb]/lbh =(s/2) /lbh = ---(2) cannot understand this line
lcm of l, b, h = lbh
ok thnx
do u understand
yes
:)
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