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.
Solution:
Given: A plastic box 1.5 m long, 1.25 m wide and 65 cm deep. It is opened at the top. The cost of 1 m² sheet is ₹20.
To find: Area of the sheet required for making the box and its cost.
Since the box is opened at the top, it has only 5 surfaces, including the 4 walls and the base. The area of the sheet required for making the cuboidal box includes the 4 walls of the box and the base.
Hence, the area of the sheet can be obtained by adding the area of the base to the lateral surface area of the cuboidal box.
Lateral surface area of cuboid = 2(l + b)h
The cost of the sheet to create the box will be equal to area of the sheet multiplied by rate of 1m² sheet.
Length, l = 1.5 m
Breadth, b = 1.25 m
Height, h = 65 cm = 65/100 m = 0.65 m
The area of the sheet required to make the box = lb + 2(l + b)h
= (1.5 m × 1.25m) + 2 × (1.25 m + 1.5 m) × 0.65 m
= 1.875 m² + 2 × 2.75 m × 0.65 m
= 1.875 m² + 3.575 m²
= 5.45 m²
Therefore, the cost of the sheet = Rate of the sheet × Area of the sheet
= ₹ 20 / m² × 5.45 m²
= ₹109
Therefore, the area of the sheet required for making the open box is 5.45 m² and the cost of the sheet is ₹109.
☛ Check: NCERT Solutions for Class 9 Maths Chapter 13
Video Solution:
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.
Class 9 Maths NCERT Solutions - Chapter 13 Exercise 13.1 Question 1
Summary:
It is given that there is a plastic box 1.5 m long, 1.25 m wide and 65 cm deep, is to be made. We have found that the area of the sheet required for making the open box is 5.45 m² and the cost of the sheet is ₹109.
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