Question

when three equal cubes are joined together the surface area of the resulting cuboid is 504 cm². find the edge of cube.

Answer 1

QUESTION


when three equal cubes are joined together the surface area of the resulting cuboid is 504 cm². find the edge of cube.



ANSWER



GIVEN


AREA OF CUBOID
$504 {cm}^{2}$

LET THE SIDE OF CUBE=X m


when 3 cube are joined then length of cuboid is 3x


and breadth and hight remain same


=>
$formula \: of \: total \: surface \: area \: of \: cuboid = 2(lb + bh + hl)$


ACCORDING TO GIVEN CONDITION

$2(lb + bh + hl) = 504 {m}^{2}$

THEREFORE



$2 \: ((3x \times x )+ (x \times x )+ \: (x \times 3x)$



$= 504$


$2(3 {x}^{2} + {x}^{2} + 3 {x}^{2} ) = 504$





$2(7 {x}^{2} ) = 504$




$7 {x}^{2} = \frac{504}{2}$




$7 {x}^{2} = 252$



${x}^{2} = \frac{252}{7}$




${x}^{2} = 36$




$x = 6m$



HENCE


SIDE OF CUBE IS =6m

so