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# A metal cube with a 6 cm edge is melted and cast into a cuboid whose base is 3.60x 0.60 cm^{2} .Calculate the height of the cuboid. Also, find the total surface area of the cuboid and cube respectively

- 422 cm
^{2}and 844.32 cm^{2} - 422.16 cm
^{2}and 216 cm^{2} - 844.32 cm
^{2} and 216 cm^{2} - 216 cm
^{2}and 211.08 cm^{2}

^{2}and 844.32 cm^{2}^{2}and 216 cm^{2}^{2}and 216 cm^{2}^{2}and 211.08 cm^{2}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 cm^{2} and 216 cm^{2}

### 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 = a^{3}

3.60 x 0.60 x h = 6^{3}

2.16 x h = 216

Dividing both sides by 2.16 we get,

h = 100

TSA of cube = 6a^{2}

= 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 cm^{2} and 216 cm^{2}.

^{3}

^{3}

Dividing both sides by 2.16 we get,

^{2}

^{2}

Therefore, the correct option is c) 844.32 cm

^{2}and 216 cm

^{2}.

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