1.

The length and breadth of a rectangular sheet of a paper are 50 cm and 30 cm, respectively. A square of side 5 cm is cut and removed form the four corners of the sheet, and the rest of the pater is folded to form a cuboid (without the top face). Find the edge of the cube whose volume is one-fourth the volume of the cuboid so formed.

Answer» Volume of the cuboid formed=`(50-2xx5)xx(30-2xx5)xx5`
`=40xx20xx5`
`=4000cm^(3)`
Let the edge of the cube be x cm.
`therefore" The volume of the cube"=x^(3)`
Given, `4x^(3)=4000`
`rArrx^(3)=1000`
`rArrx=10cm`
`therefore" The edge of the cube whose volume is equal to the cuboid formed = 10 cm"`


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