A swimming pool is 30 m long, 20 m broad and 5 m deep. Find the cost of cementing its floor and the walls at the rate of 10 per sq. metre.

Options

A. 10010
B. 10000
C. 10100
D. 11000

Answer

To solve the problem of finding the cost of cementing the floor and walls of a swimming pool, we will follow these steps:

### Step 1: Calculate the area of the floor
The area of the floor of the swimming pool can be calculated using the formula for the area of a rectangle:
\[ \text{Area of the floor} = \text{Length} \times \text{Breadth} \]
Given:
- Length = 30 m
- Breadth = 20 m

So,
\[ \text{Area of the floor} = 30 \, \text{m} \times 20 \, \text{m} = 600 \, \text{m}^2 \]

### Step 2: Calculate the area of the walls
The swimming pool has four walls. We will calculate the area of each pair of opposite walls.

1. **Area of the two longer walls** (Length = 30 m, Height = 5 m):
\[ \text{Area of two longer walls} = 2 \times (\text{Length} \times \text{Height}) = 2 \times (30 \, \text{m} \times 5 \, \text{m}) = 2 \times 150 \, \text{m}^2 = 300 \, \text{m}^2 \]

2. **Area of the two shorter walls** (Breadth = 20 m, Height = 5 m):
\[ \text{Area of two shorter walls} = 2 \times (\text{Breadth} \times \text{Height}) = 2 \times (20 \, \text{m} \times 5 \, \text{m}) = 2 \times 100 \, \text{m}^2 = 200 \, \text{m}^2 \]

### Step 3: Calculate the total area to be cemented
Now, we will add the area of the floor and the area of the walls:
\[ \text{Total area} = \text{Area of the floor} + \text{Area of the walls} \]
\[ \text{Total area} = 600 \, \text{m}^2 + (300 \, \text{m}^2 + 200 \, \text{m}^2) = 600 \, \text{m}^2 + 500 \, \text{m}^2 = 1100 \, \text{m}^2 \]

### Step 4: Calculate the cost of cementing
The cost of cementing is given at the rate of 10 per square meter. Therefore, we can calculate the total cost:
\[ \text{Total cost} = \text{Total area} \times \text{Rate per square meter} \]
\[ \text{Total cost} = 1100 \, \text{m}^2 \times 10 = 11000 \]

### Final Answer
The total cost of cementing the floor and the walls of the swimming pool is **11000**.

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