Ahmad makes cardboard boxes of two different sizes. the bigger has dimensions 20cm,15cm and 5cm and the smaller dimension 16cm,12cm and 4cm. 4% of the total surface area is required extra for all overlaps. if the cost of the card board is ₹10 for one square metre, find the cost of the cardboard for supplying 200 boxes of each kind
Answers
Answer:
The cost of larger box is Rs 197.6 and smaller box is Rs 63.232
Step-by-step explanation:
i) Bigger box:
L = 20 cm = 0.2 m
W = 15 cm = 0.15 m
H = 5 cm = 0.05 m
hence total surface area = 2(LW + LH + WH)
= 2(0.2x0.15 + 0.2x0.05 + 0.15x0.05)
= 2(0.03 + 0.01 + 0.0075)
= 0.095 m²
4% of TSA is used for overlapping = 0.04 x 0.095 = 0.0038
Hence Net card board used for 1 larger box = 0.095 + 0.0038 = 0.0988
Net card board used for 200 larger box = 200 x 0.0988 = 19.76 m²
Hence total cost of 200 box @ Rs 10 per m² = 10 x 19.76 = 197.6
ii) Smaller box
L = 16 cm = 0.16 m
W = 12 cm = 0.12 m
H = 4 cm = 0.04 m
hence total surface area = 2(LW + LH + WH)
= 2(0.16x0.12 + 0.16x0.04 + 0.12x0.04)
= 2(0.0192 + 0.0064 + 0.0048)
= 0.0304 m²
4% of TSA is used for overlapping = 0.04 x 0.0304 = 0.001216
Hence Net card board used for 1 smaller box = 0.0304 + 0.001216
= 0.031616
Net card board used for 200 smaller box = 200 x 0.031616 = 6.3232 m²
Hence total cost of 200 box @ Rs 10 per m² = 10 x 6.3232 = 63.232
Hence the cost of larger box is Rs 197.6 and smaller box is Rs 63.232
Step by step explaination of question below
