Question

Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuboid as 648 m²; find the length of the edge of each cube. Also, find the ratio between the surface area of the resulting cuboid and the surface area of a cube.

Answer 1

Let l be the length of the edge of each cube.

The length of the resulting cuboid = 4 x l = 4 l cm

Let width (b) = l cm and its height (h)= l cm

∵ The total surface area of the resulting cuboid
       = 2( l x b + b x h + h x l )

648 = 2( 4l x l + l x l + l x 4l )

4l² + l² + 4l² = 324

 9l² = 324
l² = 36
l = 6 cm

Therefore, the length of each cube is 6 cm.

`"Surface area of the resulting cuboid"/"Surface area of cube" = 648/(6l^2)`

`"Surface area of the resulting cuboid"/"Surface area of cube" = 648/[6(6)^2]`

`"Surface area of the resulting cuboid"/"Surface area of cube" = 648/216 = 3/1 = 3: 1`