Open wooden box (painted inside) — find painting rate per cm2: A wooden box, open at the top, has wall thickness 0.5 cm and outside dimensions 21 cm × 11 cm × 6 cm. The inside surfaces are painted for a total expense of ₹ 70. What is the painting rate per square centimeter?

Introduction / Context:The painting cost equals the painted inside surface area multiplied by the rate. For an open-top box, the inside painted surfaces are the base and the four inner walls, computed using inner dimensions.

Given Data / Assumptions:

• Outer: 21 × 11 × 6 cm; thickness = 0.5 cm.
• Inner dimensions: L_i = 21 − 2*0.5 = 20 cm; W_i = 11 − 2*0.5 = 10 cm; H_i = 6 − 0.5 = 5.5 cm (open top → subtract only bottom thickness).
• Cost = ₹ 70.

Concept / Approach:Inside area A_i = base + two long walls + two short walls = (L_i*W_i) + 2(L_i*H_i) + 2(W_i*H_i). Rate = Cost / A_i.

Step-by-Step Solution:Base = 20*10 = 200 cm2Two long walls = 2*(20*5.5) = 220 cm2Two short walls = 2*(10*5.5) = 110 cm2A_i = 200 + 220 + 110 = 530 cm2Rate = 70 / 530 ≈ ₹ 0.132 per cm2

Verification / Alternative check:Open top ensures no painting on the top face; inner height uses only bottom thickness.

Why Other Options Are Wrong:₹ 0.10 and ₹ 0.20 are rough-round values; ₹ 0.50 is far too high.

Common Pitfalls:Using outer dimensions for area; subtracting thickness twice on height.

Final Answer:₹ 0.132 per cm2