1. **State the problem:** We have an open rectangular box with length $1$ m, width $70$ cm, and depth $50$ cm. 2. **Convert all dimensions to meters:** - Length $l = 1$ m (already in meters) - Width $w = 70$ cm $= 0.7$ m - Depth $h = 50$ cm $= 0.5$ m 3. **Calculate the surface area to be painted:** Since the box is open at the top, painted surfaces include the base and the four sides. - Base area $= l \times w = 1 \times 0.7 = 0.7$ m$^2$ - Two longer sides area $= 2 \times (l \times h) = 2 \times (1 \times 0.5) = 1$ m$^2$ - Two shorter sides area $= 2 \times (w \times h) = 2 \times (0.7 \times 0.5) = 0.7$ m$^2$ - Total inside surface area $= 0.7 + 1 + 0.7 = 2.4$ m$^2$ 4. **Calculate outside surface area:** Outside surfaces include the base and the four sides but excluding the top (open): - Since it's open, outside includes base, sides, but not the top. - But we need the outer dimensions for outside surface calculation. Assuming the thickness is negligible, outer dimensions equal inner dimensions. - Base area $= 0.7$ m$^2$ - Two longer sides $= 1$ m$^2$ - Two shorter sides $= 0.7$ m$^2$ - Total outside surface area $= 2.4$ m$^2$ 5. **Total painted area = inside + outside area = $2.4 + 2.4 = 4.8$ m$^2$** 6. **Cost calculation:** Given cost per square meter is 90. - Total cost $= 4.8 \times 90 = 432$ **Final answer:** The cost of painting the box inside and outside is 432.