Maths-
General
Easy

Question

A metal cube with a 6 cm edge is melted and cast into a cuboid whose base is 3.60x 0.60 cm2 .Calculate the height of the cuboid. Also, find the total surface area of the cuboid and cube respectively

  1. 422 cm2and 844.32 cm2
  2. 422.16 cm2and 216 cm2
  3. 844.32 cm2 and 216 cm2
  4. 216 cm2and 211.08 cm2

Hint:

TSA of cuboid = 2[lb + bh + hl]
TSA of cube = 6x2
Volume of cube = x3
Volume of cuboid = l x b x h
where , l is length, b is breadth , h is height
x is side of cube

The correct answer is: 844.32 cm2 and 216 cm2


    We have given  edge of the metal cube a = 6cm
    Dimensions of cuboid
    Length l = 3.60
    Breadth b = 0.60
    We have to find the height of the cuboid h.
    As the both solids have same amount of material their volume will be same

    l x b x h =  a3

    3.60 x 0.60 x h = 63

    2.16 x h = 216
    Dividing both sides by 2.16 we get,

    h = 100

    TSA of cube = 6a2

    = 6(6)2

    = 6(36)

    = 216 sq.cm

    TSA of cuboid = 2[lb + bh + hl]

    = 2[(3.60)(0.60) + (0.60)(100) + (100)(3.60)]

    = 2[ 2.16 + 60 + 360 ]

    = 2[ 422.16 ]

    = 844.32 sq.cm
    Therefore, the correct option is c) 844.32 cm2 and 216 cm2.

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