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 ₹ 22,000.
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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 = = 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.
Cost of box = Cost per m3 × Volume of box
= ₹ 22,000 × 0.25
= ₹ 22,000 x
= ₹ 5,500.
Hence, cost of wood required to make the box is ₹ 5,500.
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