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प्रश्न
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.
उत्तर
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`
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