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Mathematics

The weight of a rectangular box with lid is 60 kg. The box filled with water weighs 600 kg. The weight of 1 litre of water is 1.2 kg. If the thickness of the box is 5 cm, and the external length and breadth of the box are 16 dm and 8.5 dm respectively, then the external height of the box is :

  1. 5 dm

  2. 6 dm

  3. 7 dm

  4. 8 dm

Mensuration

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Answer

Given,

External length of rectangular box = 16 dm

External breadth of rectangular box = 8.5 dm

Thickness = 5 cm = 0.5 dm

Density of water = 1.2 kg/litre

Weight of box with lid = 60 kg

Weight of box filled with water = 600 kg

Calculating the weight of the water,

Weight of the water = Weight of filled box - Weight of empty box.

= 600 - 60 = 540 kg.

Calculating the volume of water,

Volume of water = Weight of the waterDensity of the water\dfrac{\text{Weight of the water}}{\text{Density of the water}}

= 5401.2\dfrac{540}{1.2}

= 450 litres.

1 litre = 1 dm3

∴ 450 litres = 450 dm3.

Calculating internal dimensions,

Internal length = External length - 2 × Thickness

= 16 - (2 × 0.5)

= 16 - 1 = 15 dm.

Internal breadth = External breadth - 2 × Thickness

= 8.5 - (2 × 0.5)

= 8.5 - 1 = 7.5 dm.

Calculating the internal volume of rectangular box,

Volume of cuboid = l × b × h

⇒ 450 = 15 × 7.5 × h

⇒ 450 = 112.5 × h

⇒ h = 450112.5\dfrac{450}{112.5}

⇒ h = 4

∴ Internal height = 4 dm.

Calculating the external height of the box,

Since the box has thickness at both the top and bottom,

So,

External height = Internal height + 2(Thickness)

= 4 + 2(0.5)

= 4 + 1

= 5 dm.

Hence, option 1 is the correct option.

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