Utilizing a Cuboidal Lead Solid: Calculating Shots with 3 cm Diameter
In order to determine how many shots can be made from a cuboidal lead solid with dimensions of 9 cm × 11 cm, it is essential to consider the diameter of each shot. The diameter of the shots is given as 3 cm. Let's proceed with the calculation to find out the maximum number of shots that can be made from the given lead solid.
First, we need to find the volume of the cuboidal lead solid using the formula:
Volume = Length × Width × Height
Given that the dimensions of the cuboidal lead solid are 9 cm × 11 cm, and the height is not specified, we will assume the height to be h cm.
Volume = 9 cm × 11 cm × h cm
Next, we need to find the volume of a single shot. Since the shots are in the shape of cylinders, the formula for the volume of a cylinder is:
Volume of a Cylinder = π × (radius)² × height
The diameter of each shot is given as 3 cm, so the radius will be half of the diameter, i.e., 1.5 cm or 0.015 meters.
Volume of a Single Shot = π × (0.015 m)² × h cm
Now, to find the maximum number of shots that can be made from the cuboidal lead solid, we divide the volume of the lead solid by the volume of a single shot.
- Number of Shots = Volume of Cuboidal Lead Solid / Volume of a Single Shot
- Number of Shots = (9 cm × 11 cm × h cm) / (π × (0.015 m)² × h cm)
- We notice that the height (h) of the cuboidal lead solid cancels out in the division, leaving us with:
- Number of Shots = (9 cm × 11 cm) / (π × (0.015 m)²)
- Number of Shots ≈ (99 cm²) / (π × 0.000225 m²)
- Number of Shots ≈ 4400 / π
- Number of Shots ≈ 1400 (rounded to the nearest whole number)
Therefore, approximately 1400 shots can be made from a cuboidal lead solid with dimensions of 9 cm × 11 cm, where each shot has a diameter of 3 cm.
It's important to note that the calculation assumes that there is no wastage of lead during the manufacturing process. In reality, there might be some material loss during the process of making shots, which would affect the actual number of shots that can be produced from the cuboidal lead solid.
In conclusion, by considering the dimensions of a cuboidal lead solid and the diameter of each shot, we can calculate that approximately 1400 shots can be made from the given lead solid. This calculation provides valuable information for those involved in the production and utilization of lead shots for various applications.
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