Mathematics
A box 3 m long, 62.5 cm wide and 65 cm deep is to be made. It is to be open at the top. Ignoring the thickness of the sheet of which box is made, determine :
(i) area of the sheet required to make the box,
(ii) the cost of sheet used at the rate of ₹ 200 per m2.
Answer
(i) Given:
Dimension of the box:
Length (L) = 3 m
Width (W) = 62.5 cm = 0.625 m
Height (H) = 65 cm = 0.65 m
Since the box is open at the top, the total surface area required is:
Total Area = (L × W) + 2(L × H) + 2(W × H)
= (3 × 0.625) + 2(3 × 0.65) + 2(0.625 × 0.65)
= 1.875 + 2 x 1.95 + 2 x 0.40625
= 1.875 + 3.9 + 0.8125
= 6.5875 m2
Hence, the area of the sheet required to make the box = 6.5875 m2.
(ii) Rate of the sheet = ₹200 per m2
Total cost = Area x Rate
= 6.5875 x 200 = ₹1,317.50
Hence, the cost of the sheet used = ₹1,317.50.
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