A circular board radius 3 m. Painting costs ₹50/m². If 15% is unpainted, what is total cost?

The correct option is ₹1202.

Let us solve the problem step-by-step to find the total cost of painting the circular board.

Step 1: Find the total area of the circular board
The formula for the area of a circle is:

$A=\pi r^2$

Given:
Radius ($r$) = 3 m
Using $\pi \approx 3.14159$ (or $\frac{22}{7}$):

$A=3.14159\times 3^2=3.14159\times 9\approx 28.2743{\text{ m}}^2$

Step 2: Calculate the painted area
Since 15% of the board is left unpainted, the percentage of the board that is painted is:

$100\text{\%}-15\text{\%}=85\text{\%}$

Now, calculate 85% of the total area:

$\text{Painted Area}=0.85\times 28.2743\approx 24.0332{\text{ m}}^2$

Step 3: Calculate the total cost of painting
The cost of painting per square meter is ₹50/m².

$\text{Total Cost}=\text{Painted Area}\times \text{Rate per}{\text{m}}^2$

$\text{Total Cost}=24.0332\times 50\approx 1201.66$

Rounding off to the nearest rupee gives ₹1202.