Q1. A plastic box 1.5m 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:
SURFACE AREAS AND VOLUMES
EXERCISE 13.1
Q1. A plastic box 1.5m 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 cost Rs 20.
Solution:- (i).
(Given): l = 1.5 m, b = 1.25 m, h = 65 cm = 0.65 m
Method-1:
Surface Area of Cuboid = 2(lb + bh + hl)
∵ Box is to be open at the top
∴ Required Area of plastic sheet = (Surface Area of the Box) - (Area of top)
= 2(lb + bh + hl) - (l x b) [or 2(bh + hl) + lb]
= 2(1.5 x 1.25 + 1.25 x 0.65 + 0.65 x 1.5) - (1.5 x 1.25)
= 2(1.875 + 0.8125 + 0.975) - (1.875)
= 2(3.6625) - (1.875)
= 7.325 - 1.875
= 5.45 m2
Method-2:
Surface Area of Cuboid = 2(lb + bh + hl)
∵ Box is to be open at the top
∴ Required Area of plastic sheet = (Surface Area of the Box) - (Area of top)
= 2(lb + bh + hl) - (l x b)
= 2(bh + hl) + lb
= 2(1.25 x 0.65 + 0.65 x 1.5) + (1.5 x 1.25)
= 2(0.8125 + 0.975) + (1.875)
= 2(1.7875) + (1.875)
= 3.575 + 1.875
= 5.45 m2
(ii).
∵ Cost of 1m2 sheet is Rs 20
∴ Required cost of sheet for it = 5.45 x 20
= 109 Rs.
Note:- How to solve the above question in Excel
