Question

Q4. An open box of length 15m, breadth im, and height im is to be made for use on a trolly for
carrying garden waste. How much metal sheet will be required to make this box? The inside
and outside surfaces of the box are to be painted with rustproof paint. What will be the cost to
paint the box at the rate of rupees 150per square meter?​

Answer 1

Step-by-step explanation:

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 is 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 = 16 × 150 = 1950 rupees

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