What is the Cost of 1 km of Pipe at 7 Cents for Every 40 cm?

The cost of materials, particularly those used in construction and infrastructure, often needs to be calculated accurately. This article will delve into the detailed steps to calculate the cost of a 1 km length of pipe, given that each 40 cm section costs 7 cents. We will also explore the conversion from kilometers to centimeters and how to perform the necessary calculations.

Step-by-Step Calculation

1. Convert Kilometers to Centimeters

To start, it is essential to understand how to convert the given kilometer length into centimeters. One kilometer (km) is equal to 1000 meters, and each meter is 100 centimeters. Thus, the conversion from kilometers to centimeters is as follows:

1 km 1000 m 1000 * 100 cm 100000 cm

2. Determine the Number of 40 cm Sections in 100000 cm

Next, we calculate how many 40 cm sections are contained within 100000 cm. This can be done by dividing the total length in centimeters by the length of each section:

Number of sections frac{100000 cm}{40 cm} 2500

3. Calculate the Total Cost

We now multiply the number of sections by the cost per section to determine the total cost:

Total cost 2500 * 7 cents 17500 cents

4. Convert Cents to Dollars

Finally, to convert the total cost from cents to dollars, we divide by 100:

17500 cents 175 dollars

Thus, the cost of 1 km of pipe is 175 dollars.

Alternative Methods of Calculation

Method 1: Direct Division and Multiplication

Another way to approach this problem is to first find out how much the cost is for each meter and then multiply by 1000 meters in a kilometer:

100 cm 1 m, so 1000 cm 10 meters Cost of 1 m frac{7 cents}{0.40 m} 17.5 cents Cost of 1000 m (1 km) 17.5 * 100 1750 cents 175 dollars

Method 2: Using Proportions

We can set up a proportion to solve for the cost of 1 km based on the cost of 40 cm:

frac{7 cents}{40 cm} frac{x cents}{100000 cm}

Solving this proportion:

4 7 * 100000 x frac{7 * 100000}{40} 17500 cents

Converting to dollars:

17500 cents 175 dollars

Conclusion

The cost of 1 km of pipe at 7 cents for every 40 cm is 175 dollars. These steps and methods provide clear, straightforward ways to tackle such cost calculations, which are essential in various fields, including construction and infrastructure.