A Grain Silo Is Composed Of A Cylinder And A Hemisphere. The Diameter Is 4.4 Meters. The Height Of Its Cylindrical Portion Is 6.2 Meters.What Is The Approximate Total Volume Of The Silo? Use 3.14 For $\pi$ And Round The Answer To The Nearest

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Introduction

A grain silo is a crucial structure in agriculture, used to store grains and other agricultural products. The design of a grain silo typically consists of a cylindrical portion and a hemispherical top. In this article, we will explore the mathematical calculations involved in determining the total volume of a grain silo. We will use the given dimensions of a grain silo, including its diameter and height, to calculate its approximate total volume.

Understanding the Dimensions of the Grain Silo

The grain silo in question has a diameter of 4.4 meters and a height of 6.2 meters for its cylindrical portion. To calculate the volume of the silo, we need to understand the formulas for the volume of a cylinder and a hemisphere.

Volume of a Cylinder

The volume of a cylinder is given by the formula:

V_cylinder = πr^2h

where r is the radius of the cylinder and h is its height. Since we are given the diameter of the cylinder, we can calculate its radius by dividing the diameter by 2.

Calculating the Radius of the Cylinder

Given the diameter of the cylinder is 4.4 meters, we can calculate its radius as follows:

r = diameter / 2 = 4.4 / 2 = 2.2 meters

Calculating the Volume of the Cylinder

Now that we have the radius of the cylinder, we can calculate its volume using the formula:

V_cylinder = πr^2h = 3.14 × (2.2)^2 × 6.2 = 3.14 × 4.84 × 6.2 = 3.14 × 30.088 = 94.47512 cubic meters

Volume of a Hemisphere

The volume of a hemisphere is given by the formula:

V_hemisphere = (2/3)Ï€r^3

where r is the radius of the hemisphere. Since the diameter of the hemisphere is the same as the diameter of the cylinder, we can use the same radius value to calculate its volume.

Calculating the Volume of the Hemisphere

Using the radius value of 2.2 meters, we can calculate the volume of the hemisphere as follows:

V_hemisphere = (2/3)πr^3 = (2/3) × 3.14 × (2.2)^3 = (2/3) × 3.14 × 10.848 = (2/3) × 34.08328 = 22.72219 cubic meters

Calculating the Total Volume of the Silo

To calculate the total volume of the silo, we need to add the volume of the cylinder and the volume of the hemisphere.

Total Volume = V_cylinder + V_hemisphere = 94.47512 + 22.72219 = 117.19731 cubic meters

Rounding the Answer to the Nearest Whole Number

Since we are asked to round the answer to the nearest whole number, we can round the total volume to 117 cubic meters.

Conclusion

In this article, we have explored the mathematical calculations involved in determining the total volume of a grain silo. We have used the given dimensions of the silo, including its diameter and height, to calculate its approximate total volume. By understanding the formulas for the volume of a cylinder and a hemisphere, we can calculate the total volume of the silo. The total volume of the silo is approximately 117 cubic meters.

References

Introduction

In our previous article, we explored the mathematical calculations involved in determining the total volume of a grain silo. We used the given dimensions of the silo, including its diameter and height, to calculate its approximate total volume. In this article, we will answer some frequently asked questions related to calculating the volume of a grain silo.

Q: What is the formula for calculating the volume of a cylinder?

A: The formula for calculating the volume of a cylinder is:

V_cylinder = πr^2h

where r is the radius of the cylinder and h is its height.

Q: How do I calculate the radius of a cylinder?

A: To calculate the radius of a cylinder, you need to divide the diameter of the cylinder by 2.

r = diameter / 2

Q: What is the formula for calculating the volume of a hemisphere?

A: The formula for calculating the volume of a hemisphere is:

V_hemisphere = (2/3)Ï€r^3

where r is the radius of the hemisphere.

Q: How do I calculate the total volume of a grain silo?

A: To calculate the total volume of a grain silo, you need to add the volume of the cylinder and the volume of the hemisphere.

Total Volume = V_cylinder + V_hemisphere

Q: What is the significance of using 3.14 for π in the calculations?

A: Using 3.14 for π is an approximation of the actual value of π, which is approximately 3.14159. This approximation is commonly used in mathematical calculations and is sufficient for most practical purposes.

Q: Can I use a calculator to calculate the volume of a grain silo?

A: Yes, you can use a calculator to calculate the volume of a grain silo. However, it's always a good idea to understand the mathematical formulas and calculations involved to ensure accuracy and precision.

Q: What are some common applications of calculating the volume of a grain silo?

A: Calculating the volume of a grain silo is essential in various applications, including:

  • Agricultural engineering: to design and build grain silos that can store grains and other agricultural products.
  • Construction: to calculate the volume of materials needed for building grain silos.
  • Logistics: to determine the capacity of grain silos and plan transportation and storage of grains.

Q: Can I use this method to calculate the volume of other shapes, such as cones or spheres?

A: Yes, you can use similar methods to calculate the volume of other shapes, such as cones or spheres. However, the formulas and calculations may be different.

Conclusion

In this article, we have answered some frequently asked questions related to calculating the volume of a grain silo. We hope this Q&A guide has provided you with a better understanding of the mathematical calculations involved in determining the total volume of a grain silo.

References