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Mathematics

The inner dimensions of a closed wooden box are 2 m, 1.2 m and 0.75 m. The thickness of the wood is 2.5 cm. Find the cost of wood required to make the box if 1 m3 of wood costs ₹5400.

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Answer

Given,

Inner dimensions of wooden box are 2 m, 1.2 m and 0.75 m.

Thickness of the wood = 2.5 cm = 2.5100=0.025\dfrac{2.5}{100} = 0.025 m.

So the external dimensions of wooden box are,

(2 + 2 × 0.025), (1.2 + 2 × 0.025), (0.75 + 2 × 0.025)

= (2 + 0.05), (1.2 + 0.05), (0.75 + 0.5)

= 2.05 m, 1.25 m, 0.80 m.

By formula,

Volume of solid = External volume of box – Internal volume of box

Substituting the values we get,

Volume of solid = 2.05 × 1.25 × 0.80 – 2 × 1.2 × 0.75

= 2.05 – 1.80

= 0.25 m3.

Given,

1 m3 of wood costs ₹5400.

So the cost of 0.25 m3 = ₹5400 × 0.25

= 5400 × 25100\dfrac{25}{100}

= 54 × 25

= ₹1350.

Hence, cost of wood required to make the box is ₹1350.

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