A cuboid is of dimensions 60 cm × 54 cm × 30 cm . How many small cubes with side 6 cm can be placed in the given cuboid ?

The dimension of cuboid = 60 cm × 54 cm × 30 cm volume of cuboid = Length × Breadth × Height = 60 cm × 54 cm × 30 cm = 97200 cm 3 Side of cube = 6 cm The volume of a cube = side 3 = 6 3 = 216 cm 3 Number of cubes that can be placed in a given cuboid = Volume of cuboid volume of one cube = 97200 cm 3 216 cm 3 = 450 Hence, 450 cubes can be placed in the given cuboid.

Find the capacity of a rectangular cistern in litres whose dimensions are 12 . 5 m × 8 m × 4 . 2 m . Also, find the area of the iron sheet required to make the cistern.

Given that, the dimensions of a rectangular cistern are 12 . 5 m × 8 m × 4 . 2 m . We know that, Volume of a cuboid = length × breadth × height Therefore, the volume of the cistern = 12 . 5 × 8 × 4 . 2 m 3 = 420 m 3 = 420 × 1000 ∵ 1 m 3 = 1000 litres = 420000 litres Hence, the capacity of the cistern is 420000 litres . Now, the area of iron sheet that is required to make the cistern = the total surface area of the cistern. We also know that, Total surface area of cuboid = 2 ( l b + b h + h l ) So, the total surface area of the cistern = 2 ( 12 . 5 × 8 + 8 × 4 . 2 + 4 . 2 × 12 . 5 ) m 2 = 2 ( 100 + 33 . 6 + 52 . 5 ) m 2 = 372 . 2 m 2 Hence, the area of the iron sheet required to make the cistern is 372 . 2 m 2 .