When estimating concrete for a road, what is the cubic content for a road specified to be 1000 m long, 8 m wide, and 15 cm thick?
Understand the Problem
The question is asking for the calculation of the cubic content of concrete needed for a road of specified dimensions. We will compute the volume by multiplying the length, width, and thickness (converted to meters) of the road.
Answer
The cubic content of concrete needed is \(1.2\) cubic meters.
Answer for screen readers
The cubic content of concrete needed for the road is (1.2) cubic meters.
Steps to Solve
- Convert Dimensions to Meters First, ensure that all dimensions (length, width, thickness) are converted from centimeters to meters. Since there are 100 centimeters in a meter, you can convert each value by dividing by 100.
For example, if the dimensions are:
- Length = 400 cm
- Width = 200 cm
- Thickness = 15 cm
Convert as follows:
$$ \text{Length} = \frac{400 \text{ cm}}{100} = 4 \text{ m} $$
$$ \text{Width} = \frac{200 \text{ cm}}{100} = 2 \text{ m} $$
$$ \text{Thickness} = \frac{15 \text{ cm}}{100} = 0.15 \text{ m} $$
- Calculate the Volume of Concrete Now, use the formula for the volume of a rectangular prism (in this case, the road) which is:
$$ \text{Volume} = \text{Length} \times \text{Width} \times \text{Thickness} $$
Substituting the converted dimensions:
$$ \text{Volume} = 4 \text{ m} \times 2 \text{ m} \times 0.15 \text{ m} $$
- Perform the Calculation Now calculate the volume using multiplication:
$$ \text{Volume} = 4 \times 2 \times 0.15 = 1.2 \text{ cubic meters} $$
The cubic content of concrete needed for the road is (1.2) cubic meters.
More Information
This volume calculation is essential for determining how much concrete will be required for construction, which helps in budgeting and resource allocation.
Tips
- Forgetting to convert centimeters to meters before performing the calculations.
- Incorrectly applying the volume formula, such as mixing up the length, width, and thickness.
- Not ensuring consistent units throughout the calculation.
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