The outer dimensions of a closed box is 15 cm by 13 cm by 10 cm. Thickness of the wood is 2 cm. Find the total cost of wood required to make the box, if 1 cm3 of wood costs ₹ 5.00.
Answers
The total cost of wood required to make the box, if 1 cm3 of wood costs ₹ 5.00, is ₹ 6780.
Step-by-step explanation:
Step 1:
The outer dimensions of the closed box are given as:
Outer Length = 15 cm
Outer Breadth = 13 cm
Outer Height = 10 cm
∴ Outer volume of the closed box = Length x Breadth x Height = 15 * 13 * 10 = 1950 cm³
Step 2:
The thickness of the wood = 2 cm
So, the inner dimensions of the box are given as:
Inner Length = outer length – (2*width) = 15 – (2*2) = 15 – 4 = 11 cm
Inner Breadth = outer breadth – (2*width) = 13 – (2*2) = 13 – 4 = 9 cm
Inner Height = outer height – (2*width) = 10 – (2*2) = 10 – 4 = 6 cm
∴ Inner volume of the closed box = length x breadth x height = 11 * 9 * 6 = 594 cm³
Step 3:
Now,
The volume of the wood is given by,
= [Outer volume of the closed box] – [Inner volume of the closed box]
= 1950 - 594
= 1356 cm³
Step 5:
The cost of 1 cubic cm of wood is given as ₹ 5.00.
Thus,
The total cost of wood required to make the box is,
= 1356 cm³ * ₹ 5
= ₹ 6780
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Answer: ₹ 6780
Step-by-step explanation:
Given ,
The outer length = 15 cm
The outer breadth = 13 cm
The outer height = 10 cm
Thickness of the wood = 2 cm
Cost of wood per m² = ₹ 5.00
Therefore ,
Inner length = {15-(2+2)} cm = {15-4} cm= 11 cm
Inner breadth = {13-(2+2)} cm = {13-4}cm = 9 cm
Inner height = {10-(2+2)} cm = {10-4}cm = 6 cm
Therefore ,
The outer volume = l×b×h = (15×13×10) cm³ = 1950 cm³
The inner volume = l×b×h =(11×9×6) cm³ = 594 cm ³
Therefore ,
The volume of the wood = ( outer volume ) - ( inner volume ) = (1950-594) cm³ = 1356 cm³
Therefore ,
The total cost of the required wood = ₹ ( 1356×5) = ₹ 6780
Therefore ,
The answer is ₹ 6780
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