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).
Doubt by Hitanshi
Solution : Coming Soon
Let
Length of cuboid = a
Breadth of cuboid = b
Height of cuboid = c
Surface area of cuboid = S = 2(ab+bc+ca)
Volume of the cuboid = V = abc
Now, 1/V = 2/S (1/a+1/b+1/c)
RHS
2/S(1/a+1/b+1/c)
= 2/S[(bc+ac+ab)/abc].
= 1/S[2(bc+ac+ab)/abc]
= 1/S[2(ab+bc+ca)/abc]
= 1/S[S/abc] [∵2(ab+bc+ca=S]
= 1/abc
= 1/V [∵abc=V]
= LHS
∴ LHS=RHS
Hence Proved.