The inner dimensions of wooden box are 2m, 1.2m, 0.75m. the thickness of wood is 2.5cm.find the cost of wood if the cost of wood of 1cubic metre is rs.5400
assuming that the wood purchased will be used efficiently, the volume of wood is the outside volume less the inside volume. Since there are parallel sides, the inner dimensions are 5 cm less than the outer. Thus, the volume of wood is
(200-5)(120-5)(75-5) = 1569750 cm^3 = 1.56975 m^3
Now use that to find the cost
yes
1350
To find the cost of the wood, we first need to calculate the volume of the wooden box and then determine the thickness of the wood used.
The given inner dimensions of the wooden box are:
Length = 2m
Width = 1.2m
Height = 0.75m
We can calculate the volume of the wooden box using the formula:
Volume = Length × Width × Height
Substituting the given values:
Volume = 2m × 1.2m × 0.75m
= 1.8 cubic meters
Now, we need to consider the thickness of the wood. The thickness is given as 2.5cm, but we need it in meters to maintain consistency with the volume.
Converting the thickness to meters:
Thickness = 2.5cm ÷ 100 (since 1m = 100cm)
= 0.025m
To find the volume of the wood, we need to subtract the volume of the inner space from the volume of the overall box.
Volume of the wood = (Volume + 2 × Thickness × (Length × Width + Width × Height + Height × Length))
Substituting the values:
Volume of the wood = [1.8 + 2 × 0.025 × (2 × 1.2 + 1.2 × 0.75 + 0.75 × 2)]
= [1.8 + 2 × 0.025 × (2.4 + 0.9 + 1.5)]
= [1.8 + 2 × 0.025 × 4.8]
= [1.8 + 2 × 0.12]
= [1.8 + 0.24]
= 2.04 cubic meters
Now, we can calculate the cost of the wood using the given rate:
Rate of wood per cubic meter = Rs. 5400
Cost of the wood = Volume of the wood × Rate of wood per cubic meter
= 2.04 cubic meters × Rs. 5400
= Rs. 11,016
Therefore, the cost of the wood for the given wooden box is Rs. 11,016.