An open box is made of wood 3 cm thick. Its external length, breadth and height are 146 cm, 116 cm and 83 cm respectively. Find the cost of painting the inner surface at Rs 2 per 1000 sq. cm.

the box is as shown in figure

The wood is 3 cm thick

And given length, breadth and height are external which means including the wood thickness

So, to find the inner surface area we need to subtract the wooden thickness from external length, breadth and height

Thus length, breadth and height of inner surface area are as follows

In the length and breadth, we need to subtract 3 from both the sides which means we have to subtract 6 but in the height as the box is open from one end so we need to subtract only 3cm base thickness as seen in the figure

Length = 146 – 6 = 140 cm

Breadth = 116 – 6 = 110 cm

Height = 83 – 3 = 80 cm

The shape of the box is a cuboid and it is open box, therefore, we should subtract the top rectangular surface area from the total inner surface area

Total surface area of cuboid = 2 × (lb + bh + lh) – lb

⇒ total surface area of box = 2 × (140×110 + 110×80 + 140×80) – 140×110

= 2 × (15400 + 8800 + 11200) – 15400

= 2 × 35400 – 15400

= 70800 – 15400

= 55400 cm²

Cost of painting 1000 cm² is Rs 2

Thus, cost of painting 55400 cm² =

= 55.4 × 2

= 110.8 Rs

Therefore, cost of painting the inner surface = 110.8 Rs