The outer dimensions of a closed wooden box are 10 cm by 8 cm by 7cm. Thickness of the wood is 1 cm. Find the total cost of the wood required to make box if 1 cm3 of wood cost 2 rupees.
Answers
Outer breadth = 8 cm
Outer height = 7 cm
Outer volume = length × breadth × height
= 10 × 8 × 7 = 560 cm3
Thickness of wooden box, w = 1 cm
Inner length = l – 2w = 10 – 2 = 8 cm
Inner breadth = b – 2w = 8 – 2 = 6 cm
Inner height = h – 2w = 7 – 2 = 5 cm
Outer volume = 8 × 6 × 5 = 240 c m3
Volume of wood used = outer volume – inner volume
= 560 – 240 = 320 cm3
Given cost of 1 cm3 of wood = Rs 2
Hence the total cost of wood required = Rs 2 × 320
= Rs 640
Given:
The dimensions of a closed wooden box is 10cm×8cm×7cm.
Thickness of the wood is 1cm.
To Find:
The cost of the wood required to make box if 1cm³ of wood cost Rs.2.
Solution:
Length of the wooden box(outer) = 10cm
Breadth of the wooden box(outer) = 8cm
Height of the wooden box(outer) = 7cm
Outer volume of the wooden box = length × breadth × height
= 10 × 8 × 7
= 560cm³
It is given that the thickness of the wooden box = 1cm
Inner length of the wooden box = length - 2w
= 10 - 2w
= 8 cm
Inner width of the wooden box = b -2w
= 8 -2
= 6cm
Inner height of the wooden box = h - 2w
= 7 - 2
= 5cm
Outer volume of the wooden box = length × breadth × height
= 8 × 6 × 5
= 240 cm³
So, the volume of the wooden box = outer volume - inner volume
= 560 - 240
= 320cm³
Cost of 1cm³ of the wood = Rs.2
Total cost of wood required = Rs.2 × 320
= Rs.640
Therefore, the cost of wood is Rs.640.