Question

An open box of length 1.5 m, breadth 1 m, and height 1 m is to be made for use on a trolley for carrying garden waste. How much sheet metal will be required to make this box? The inside and outside surface of the box is to be painted with rust-proof paint. At a rate of 150 rupees per sqm, how much will it cost to paint the box?

Answer 1

Length of the open box, l = 1.5 m

Breadth of the open box, b = 1 m

Height of the open box, h = 1 m

Surface area of open box = Total surface area of the box − Area of the top

= 2(l × b + b × h + h × l) − l × b

= 2(1.5 × 1 + 1 × 1 + 1 × 1.5) − 1.5 × 1

= 2(1.5 + 1 + 1.5) − 1.5

= 2 × 4 − 1.5

= 8 − 1.5

= 6.5 m²

Hence, 6.5 m² of the sheet will be needed to make the open box.

Now, it is given that the inside and the outside surface of the open box are to be painted with rust-proof paint.

∴ Total area of the box to be painted = 2 × Surface area of open box

= 2 × 6.5

= 13 m²

Now, the cost of the painting of 1 m² of area = 150 rupees

∴ Cost of painting of 13 m² of area = 13 × 150 = 1950 rupees

Hence, it will cost 1950 rupees to paint the open box from inside and outside with rust-proof paint.