A circular signboard has a radius of 2 m. If painting costs ₹60 per m² and 10% of the board is left unpainted, what is the total painting cost?

Correct — B. Find the board's area, keep the 90% that is painted, then apply the rate.

Board area: πr² = π × 2² = 4π m²
Painted share, 100% − 10% = 90%: 0.9 × 4π = 3.6π m²

Cost at ₹60 per m²: 3.6π × 60 = 216π
With π ≈ 3.1416: 216 × 3.1416 ≈ ₹678.6 → option (b)

Why the others are wrong

• (a)
  ₹658.2 — ₹658.2 pays for only about 10.97 m² (658.2 ÷ 60), but the painted part is 90% of 4π ≈ 12.57 m², which is 11.31 m².
• (c)
  ₹630.4 — ₹630.4 pays for only about 10.51 m² (630.4 ÷ 60), well short of the 11.31 m² that is painted, 90% of the 12.57 m² board.
• (d)
  ₹681.9 — ₹681.9 pays for 11.365 m² (681.9 ÷ 60), a little more than the 11.31 m² painted. Even π = 22⁄7 only reaches ₹678.86.

A painting cost is area × rate per unit area. Any part left unpainted comes off the area before the rate is applied.

Collecting the constants first keeps it to one multiplication by π: 0.9 × 60 × π × 2² = 54 × 4π = 216π ≈ ₹678.6.

Key facts

• Area of a circle = πr², so a 2 m radius gives 4π ≈ 12.57 m².
• Leaving 10% unpainted means paying for 90% of the area, 11.31 m² here.
• Painting and tiling charge by area (m²), while fencing charges by length of boundary (m).

Common traps

• Charging ₹60 on the whole 4π m²: that gives about ₹754, the cost before the unpainted 10% is removed.
• Using 2πr in place of πr²: at r = 2 both equal 4π, so the slip goes unnoticed here and fails at any other radius.

No directly related past PYQ was found.