A construction company has dump trucks that hold 35 cubic yards. If the company’s workers dig

a cylindrical hole with height 10 feet and radius 20 feet, then how many dump truck loads will

they need to haul away the dirt they dug out from the hole? Explain your reasoning.

To solve this problem, we'll calculate the volume of the cylindrical hole and then determine how many dump truck loads are required to haul away the dirt.

### Step 1: Convert dimensions to consistent units
First, convert the height and radius of the cylinder from feet to yards, since the dump trucks hold 35 cubic yards. There are 3 feet in 1 yard.

\[
\text{Height} = \frac{10 \text{ feet}}{3} \approx 3.33 \text{ yards}
\]
\[
\text{Radius} = \frac{20 \text{ feet}}{3} \approx 6.67 \text{ yards}
\]

### Step 2: Calculate the volume of the cylindrical hole
The volume \(V\) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
Where:
- \(r\) is the radius of the base (in yards)
- \(h\) is the height of the cylinder (in yards)

Substitute the values:
\[
V = \pi (6.67 \text{ yards})^2 \times 3.33 \text{ yards}
\]

Calculating the volume:
\[
V = \pi \times 44.49 \text{ square yards} \times 3.33 \text{ yards} \approx \pi \times 148.15 \text{ cubic yards}
\]
\[
V \approx 465.42 \text{ cubic yards}
\]

### Step 3: Determine the number of dump truck loads
Each dump truck holds 35 cubic yards, so the number of truckloads required is:
\[
\text{Number of truckloads} = \frac{465.42 \text{ cubic yards}}{35 \text{ cubic yards per truckload}} \approx 13.3
\]

Since you can't have a fraction of a truckload in practice, the company will need to round up to the nearest whole number:
\[
\text{Number of truckloads} = 14 \text{ truckloads}
\]

### Final Answer:
The construction company will need 14 dump truck loads to haul away the dirt.

Would you like more details or have any questions?

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Here are 8 related questions:
1. How do you convert between cubic feet and cubic yards?
2. What is the formula for the volume of a cylinder, and why does it work?
3. If the radius or height were different, how would the calculation change?
4. How do you determine the number of trips required when dealing with partial loads?
5. What are the units of measurement for volume, and how do they relate?
6. How would this problem change if the dump truck capacity was in cubic feet?
7. How can you estimate the number of truckloads if the radius and height are given in different units?
8. What is the significance of rounding up in real-world applications?

**Tip:** When calculating practical problems involving transportation or logistics, always round up the number of trips to ensure all materials are accounted for.

Learn how to calculate the number of dump truck loads needed to haul dirt from a cylindrical hole with a height of 10 feet and a radius of 20 feet. Includes step-by-step volume calculation and practical truckload determination. Suitable for Grades 7-9.

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