Along a path, 25 conical pillars are constructed. Each pillar has radius 15 cm and height 20 cm. Find the total cost of painting these pillars at the rate of Rs. 50 per`" cm"^2`. [ Take `pi = 3.14` ]

Options

A. Rs. 201752.50
B. Rs. 2052325
C. Rs. 3214325.50
D. Rs. 1471875

Answer

To solve the problem of finding the total cost of painting the conical pillars, we will follow these steps:

### Step 1: Calculate the Curved Surface Area (CSA) of One Conical Pillar
The formula for the curved surface area of a cone is given by:
\[ \text{CSA} = \pi r l \]
where \( r \) is the radius and \( l \) is the slant height of the cone.

First, we need to find the slant height \( l \) using the Pythagorean theorem:
\[ l = \sqrt{r^2 + h^2} \]
where \( h \) is the height of the cone.

Given:
- Radius \( r = 15 \) cm
- Height \( h = 20 \) cm

Calculating \( l \):
\[ l = \sqrt{15^2 + 20^2} = \sqrt{225 + 400} = \sqrt{625} = 25 \text{ cm} \]

Now, substituting \( r \) and \( l \) into the CSA formula:
\[ \text{CSA} = \pi \times 15 \times 25 \]
Using \( \pi = 3.14 \):
\[ \text{CSA} = 3.14 \times 15 \times 25 = 3.14 \times 375 = 1177.5 \text{ cm}^2 \]

### Step 2: Calculate the Total Curved Surface Area for 25 Pillars
Since there are 25 pillars, the total curved surface area will be:
\[ \text{Total CSA} = 25 \times \text{CSA} = 25 \times 1177.5 = 29437.5 \text{ cm}^2 \]

### Step 3: Calculate the Total Cost of Painting
The cost of painting is given at the rate of Rs. 50 per cm². Therefore, the total cost will be:
\[ \text{Total Cost} = \text{Total CSA} \times \text{Cost per cm}^2 = 29437.5 \times 50 \]
Calculating the total cost:
\[ \text{Total Cost} = 1471875 \text{ Rs} \]

### Final Answer
The total cost of painting the 25 conical pillars is Rs. 1471875.