Question

Every year about 20,000 pounds of stone, sand and gravel are mined for each person in the United States. a. Calculate how many pounds of stone, sand, and gravel will be needed for an individual during an 80 -year lifespan. b. If one cubic yard of rock weighs roughly 1700 pounds, how big a hole (cubic yards) must be dug to supply an individual with 80 years' worth of stone, sand, and gravel? c. A typical pickup truck can carry about a half cubic yard of rock. How many pickup truck loads would be necessary during the 80 -year span?

Short answer

80-year lifespan needs 1,600,000 pounds, 941.18 cubic yards, or 1883 truckloads.

Step-by-step solution

Calculate Total Pounds for 80 Years

To calculate the total pounds of stone, sand, and gravel needed for an individual over an 80-year lifespan, multiply the annual amount by 80. Thus, \(20,000 \text{ pounds/year} \times 80 \text{ years} = 1,600,000 \text{ pounds}\).

Convert Pounds to Cubic Yards

Next, we need to convert the total pounds into cubic yards, knowing that 1 cubic yard of rock weighs approximately 1700 pounds. Divide the total pounds by the weight per cubic yard: \(\frac{1,600,000 \text{ pounds}}{1700 \text{ pounds/cubic yard}} \approx 941.18 \text{ cubic yards}\).

Calculate Pickup Truck Loads

A typical pickup truck can carry about half a cubic yard of rock. To find out how many truckloads are needed, divide the total cubic yards by 0.5: \(\frac{941.18 \text{ cubic yards}}{0.5 \text{ cubic yards/truck}} = 1882.36 \text{ truckloads}\). Since the number of truckloads must be whole, round up to 1883 truckloads.

Key concepts

Mineral Resources

Mineral resources, such as stone, sand, and gravel, play a crucial role in our daily lives. They are essential raw materials for construction, infrastructure, and various industries. From the roads you drive on to the buildings you work in, these resources are ever-present.
Each year, a significant amount of these materials is mined to meet the needs of the population. For instance, in the United States, approximately 20,000 pounds of stone, sand, and gravel are extracted annually per person. Over a typical 80-year lifespan, this adds up to an individual requiring about 1,600,000 pounds of these materials.

• Stone is often used for strong foundations and structural parts of buildings.
• Sand is a primary component in concrete and is also used in road construction.
• Gravel, with its high durability, is perfect for roads and driveways.

As populations continue to grow, the demand for these critical materials is expected to increase, leading to more extensive mining operations and more profound impacts on the environment. Understanding the lifecycle and utilization of mineral resources is vital for promoting sustainable practices.

Volume Measurement

Understanding volume measurement is essential, especially when dealing with large-scale materials like stone, sand, and gravel. Volume helps determine the space a substance occupies, and when it comes to mineral resources, this is often measured in cubic yards.
A cubic yard is a volume measurement equivalent to a cube with sides measuring one yard each. This unit is typical in construction and transport, especially for aggregates like rock and sand.
To calculate how much material is required in terms of volume, first, you convert from weight to volume. For example, if a single cubic yard of rock weighs about 1700 pounds, converting the weight of mineral resources into cubic yards involves dividing the total pounds by this weight. This tells us how many cubic yards are needed.

• Volume conversion is crucial for project planning in construction.
• Average conversion rates (like pounds to cubic yards) can vary based on material density.

These conversions are not only important for logistics but also for budgeting and resource management in industries like construction and mining.

Mathematical Calculations

Mathematical calculations simplify complex real-world problems, such as determining the number of resources needed for a lifetime. By using basic arithmetic and unit conversions, one can easily estimate volumes and requirements.

For instance, the calculation begins by determining the total material needed over 80 years. This is done by multiplying the annual requirement by the number of years to get the total pounds required. From there, the conversion from pounds to cubic yards helps gauge the physical space needed.
For example: \[ 20,000 ext{ pounds/year} \times 80 ext{ years} = 1,600,000 ext{ pounds} \]Next, convert the total weight into cubic yards:\[ \frac{1,600,000 ext{ pounds}}{1700 ext{ pounds/cubic yard}} \approx 941.18 ext{ cubic yards} \] Finally, determining the number of truckloads involves further division:\[ \frac{941.18 ext{ cubic yards}}{0.5 ext{ cubic yards/truck}} = 1882.36 \], which rounds up to 1883 truckloads for practicality.

• Begin with total need in pounds to simplify the start.
• Perform unit conversions to understand real-world implications.
• Round up as necessary to ensure full coverage in transport or capacity calculations.

By breaking down calculations into these steps, any complex problem can become manageable and more understandable, facilitating better planning and resource utilization.