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
Answers
Answer:
Step-by-step explanation:
(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
AnswEr :
- Length = 1.5 m = 150 cm
- Breadth = 1.25 m = 125 cm
- Height = 65 cm
⋆ Refrence of Image is in the attachment :
( i ) The area of the sheet required for making the box.
⇒ Area Required = TSA - Area of Top
⇒ Area Required = 2(lb + bh + hl) - lb
⇒ Area Required = 2lb + 2bh +2hl - lb
⇒ Area Required = lb + 2bh + 2hl
⇒ Area Required = (150 × 125) + [2 × (125 × 65)] + [2 × (65 × 150)]
⇒ Area Required = 18,750 + (2 × 8,125) + (2 × 9,750)
⇒ Area Required = 18,750 + 16,250 + 19,500
⇒ Area Required = 54,500 cm²
- Dividing it by (100 × 100)
⇒Area Required = 5.45 m²
∴ Area of Sheet Required is 5.45 m²
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(ii) The cost of sheet for it, if a sheet measuring 1m² costs Rs 20
⇒ Cost of Sheet = Area Required × Rate
⇒ Cost of Sheet = 5.45 m² × Rs. 20
⇒ Cost of Sheet = Rs. 109
∴ Cost of Sheet Required is Rs. 109
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