Question

If V is the volume of a cuboid of dimensions x , y and z and A is its Surface area, then A/V is

a) x²y²z²
b) 1/2(1/xy + 1/yz + 1/xz)
c)1/2(1/x + 1/y + 1/z)
d) 1/xyz

[ Method required ]

Answer 1

$\bf HELLO \: \: DEAR,$

$\bf GIVEN \: \: THAT:-$

$\bf dimensions \: \: of \: \: cuboid = x , y , z \\ \\ \bf \: where,\\ \\ \bf length = x , breath = y , height = z \\ \\ \: \: \: \: \: \: \\ \\ \boxed{\bf now,}$

$\bf V = volume \: \: of \: \: cuboid = length * breadth * height = x*y*z = (xyz) \\ \\ \\ \bf \: and, \: \: A = surface \: \: area \: \: of \: \: cuboid = 2(lb + bh + lh) \\ \\ \\ \bf = 2(xy + yz + xz)$

$\bf \: hence , A/V \\ \\ \bf \: = 2(xy + yz + xz)/xyz \\ \\ \bf \: = 2(xy/xyz + yz/xyz + xz/xyz) \\ \\ \bf \: = 2(1/z + 1/x + 1/y)$

$\underline{\bf I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, \: \: THANKS}$