Question

ABCD is the cross-section of a metal container in a paint factory.

If AB = 2.4 m, DC = 1.6 m, BQ = CR = 1.2 m and height of the container is 1.1 m, find 

1. the volume of paint in the container.
2. the cost of paint at ₹ 40 per litre. [1m³ = 1000 litres]

Answer 1

Given:

• AB = 2.4 m
• DC = 1.6 m
• BQ = CR = 1.2 m
• Height of container = 1.1 m
• Cost of paint = ₹ 40 per litre
• 1 m³ = 1000 litres

1. The cross-section ABCD is not a trapezium as initially assumed, but a parallelogram with base AB (2.4 m) and height BQ (1.2 m).

Since BQ = CR = 1.2 m, the vertical height between AB and DC is 1.2 m (not the sum 2.4 m).

2. Calculate area of parallelogram ABCD:

Area = base × height

= AB × BQ

= 2.4 m × 1.2 m

= 2.88 m²

3. The given length (height of the container) is 1.1 m along direction perpendicular to the cross-section.

So Volume = Area of cross section × height

= 2.88 m² × 1.1 m

= 3.168 m³

4. But from the figure, DC = 1.6 m seems to be the length of cross-section along the base. 

So the average length used is average of AB and DC Average base length.

= `(2.4 + 1.6)/2` 

= 2.0 m 

Using this and height of 1.2 m for cross-section height gives area:

Area = Base × Height

= 2.0 m × 1.2 m

= 2.4 m²

Volume = 2.4 m² × 1.1 m

= 2.64 m³

5. Cost: Volume in litres = 2.64 m³ × 1000 = 2640 litres

Cost = 2640 × 40 = ₹105600

The volume is 2.64 m³ using the average base length 2.0 m × height 1.2 m of cross section and container height 1.1 m. 

The cost of paint is ₹ 105600 at ₹ 40 per litre.