Verified answer

Answer:

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

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

Therefore, the cost of the sheet = Rate of the sheet × Area of the sheet= ₹ 20 / 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.