Q. 14.1( 615 Votes )

A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine:
(i) The area of the sheet required for making the box.
(ii) The cost of sheet for it, if a sheet measuring 1m2 costs Rs 20

Answer :


(i) Box is to be open at top (Pink color in the above diagram shows that the box is open)
Method 1:
Lateral Surface Area = Area of the four sides of the cuboid (Area of four rectangles on the sides) = 2 (length x height) + 2(width x height)

Area of sheet required = lateral Surface Area + Area of the base = 2 l h + 2 b h + l b

= [2 × 1.5 × 0.65 + 2 × 1.25 × 0.65 + 1.5 × 1.25] m2

= (1.95 + 1.625 + 1.875) m2
= 5.45 m2

 (ii) Cost of sheet per m2 area = Rs 20

Cost of sheet of 5.45 m2 area = Rs (5.45 × 20)

= Rs 109


Method 2:
(i) Area of Sheet Required = Total Surface Area - Area of top
Area of Sheet Required = 2(lb + bh + hl) - lb
Area of sheet Required = 2 × 1.5 × 0.65 + 2 × 1.25 × 0.65 + 2 × 1.5 × 1.25 - 1.5 × 1.25
Area of Sheet Required = 5.45 m2


 (ii) Cost of sheet per m2 area = Rs 20

Cost of sheet of 5.45 m2 area = Rs (5.45 × 20)

= Rs 109
Hence, the cost of sheet is Rs. 109.

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