A cubical wooden box of internal edge 1 m is made of 5 cm thick wood. The box is open at the top. If the wood costs ₹ 28,800 per cubic metre, find the cost of the wood required to make the box. Calculate the cost to nearest hundred rupees.

Given,

Internal edge of cubical wooden box = 1 m

Thickness of wood = 5 cm = $\dfrac{5}{100}$ m = 0.05 m

We know that,

External length = (1 + 0.05 × 2) = 1.1 m

External Breadth = (1 + 0.05 × 2) = 1.1 m

External Height = (1 + 0.05) = 1.05 m [Since, box is open at top]

By formula,

Volume of the wood used = Outer volume – Inner volume

Substituting the values we get,

Volume of the wood used = 1.1 × 1.1 × 1.05 – 1 × 1 × 1

= 1.2705 – 1

= 0.2705 m³

Given,

Cost of 1 m³ of wood = ₹ 28,800

Cost of the wood required to make the box = Cost of wood per m³ × Volume of wood

= ₹ 28,800 × 0.2705

= ₹ 7,790.40

≈ ₹ 7,800 (to nearest hundred)

Hence, cost of wood required to make the box = ₹ 7,800.