A water tank is made of an aluminum sheet 3 cm thick. The tank is open at the top. Its external dimensions are 1.36 m, 1.06 m and height 0.83 m. What is the cost of painting the inner surface of the tank at 50 paise per 100 sq. cm?

Correct option is C

Given:

Thickness of the aluminium sheet = 3 cm = 0.03 m

External dimensions of the tank:

Length = 1.36 m

Width = 1.06 m

Height = 0.83 m

Cost of painting = 50 paise per 100 sq. cm

Concept Used:

The cost of painting the inner surface is based on the area of the inner surface of the tank. The inner dimensions will be reduced by the thickness of the aluminium sheet on each side.

Formula Used:

Inner dimensions:

Inner length = External length - 2 × Thickness

Inner width = External width - 2 × Thickness

Inner height = External height - Thickness

Area of the inner surface of the tank = 2 × (Length × Height + Width × Height) + Length × Width

Cost = Area to be painted × Cost per unit area

Solution:

Inner dimensions:

Inner length = 1.36 m - 2 × 0.03 m = 1.30 m

Inner width = 1.06 m - 2 × 0.03 m = 1.00 m

Inner height = 0.83 m - 0.03 m = 0.80 m

Area of the inner surface:

Area = 2 × (1.30 × 0.80 + 1.00 × 0.80) + 1.30 × 1.00

= 2 × (1.04 + 0.80) + 1.30

= 2 × 1.84 + 1.30

= 3.68+1.30 = 4.98 m²

Converting the area into square centimetres:

4.98 m² = 4.98 × 100 cm² = 49800 cm²

Cost of painting:

​$$\text{Cost} = \frac{50 \, \text{paise}}{100 \, \text{sq. cm}} \times 49800 \, \text{sq. cm}\\ \ \\= 50 \times \frac{49800}{100} \\ \ \\= 50 \times 498 = 24900 \, \text{paise} = 249 \, \text{rupees}$$​​

Thus, The cost of painting the inner surface of the tank is ₹249.