1. . 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 1 m^2 costs Rs. 20.
.
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Answers
Answer:
Surface area:
Surface area of a solid object is a measure of the total area that the surface of the object occupies and it is always measured in square unit.
Hence surface area is also known as total surface area TSA.
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Given:
Length of plastic box (l)= 1.5 m
Width of plastic box(b) = 1.25 m
Depth of plastic box(h) = 65cm = 65/100=0.65m
(i) The area of sheet required to make the box= surface area of the box including the base & excluding the top.
[Box is open at the top]
Surface area of the box = Lateral surface area + Area of the base
= 2(l+b)×h + (l×b)
= 2[(1.5 + 1.25)×0.65] + (1.5 × 1.25)
= 2(2.75)× 0.65 +1.875
=(3.575 + 1.875)
= 5.45 m²
The sheet required required to make the box is 5.45 m²
(ii) Cost of 1 m² of sheet = ₹ 20
Cost of 5.45 m² of sheet = ₹ (20 × 5.45)
= ₹109
Cost of 5.45 m² of sheet = ₹ 109
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Question :-
A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is opened 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 ₹20.
Answer :-
(i) Here, length (l) = 1.5 m, bread th(b) = 1 .25 m
and height (h) = 65 cm = 65/100 m = 0.65 m
∵ It is open from the top.
∴ Its surface area
= [Lateral surface area] + [Base area]
= [2(1 + b)h] + [lb]
= [2(1.50 + 1.25)0.65] m2 + [1.50 x 1.25] m2
= [2 x 2.75 x 0.65] m2 + [1.875] m2
= 3.575 m2+ 1.875 m2 = 5.45 m2
∴ Area of the sheet required for making the box = 5.45 m2
(ii) Cost of 1 m2 sheet = Rs. 20
Cost of 5.45 m2 sheet = Rs. (20 x 5.45)
= Rs. 109
Hence, cost of the required sheet = Rs. 109
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