The Figure Shows A Drinking Trough In The Shape Of A Half-cylinder. Find Its Capacity In Litres. 15 Cm 84 Cm​

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Introduction

In this article, we will explore the concept of finding the capacity of a half-cylinder shaped drinking trough. The trough has a height of 84 cm and a diameter of 15 cm. We will use the formula for the volume of a cylinder to find the capacity of the trough, and then multiply it by 2 to account for the half-cylinder shape.

Understanding the Problem

The problem requires us to find the capacity of a half-cylinder shaped drinking trough. The trough has a height of 84 cm and a diameter of 15 cm. To find the capacity, we need to use the formula for the volume of a cylinder, which is given by:

V = πr^2h

where V is the volume, π is a constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.

Finding the Radius of the Cylinder

The diameter of the cylinder is given as 15 cm. To find the radius, we need to divide the diameter by 2.

r = diameter / 2 = 15 / 2 = 7.5 cm

Finding the Volume of the Cylinder

Now that we have the radius, we can use the formula for the volume of a cylinder to find the volume of the full cylinder.

V = πr^2h = π(7.5)^2(84) = 3.14(56.25)(84) = 18,444.6 cubic cm

Finding the Capacity of the Half-Cylinder

Since the trough is a half-cylinder, we need to multiply the volume of the full cylinder by 2 to find the capacity of the half-cylinder.

Capacity = 2V = 2(18,444.6) = 36,889.2 cubic cm

Converting the Capacity to Litres

To convert the capacity from cubic cm to litres, we need to divide the capacity by 1000.

Capacity (litres) = 36,889.2 / 1000 = 36.8892 litres

Conclusion

In this article, we have found the capacity of a half-cylinder shaped drinking trough with a height of 84 cm and a diameter of 15 cm. We used the formula for the volume of a cylinder to find the volume of the full cylinder, and then multiplied it by 2 to account for the half-cylinder shape. Finally, we converted the capacity from cubic cm to litres.

Mathematical Formulas Used

  • V = πr^2h (formula for the volume of a cylinder)
  • r = diameter / 2 (formula for finding the radius of a cylinder)
  • Capacity = 2V (formula for finding the capacity of a half-cylinder)

Key Concepts

  • Volume of a cylinder
  • Radius of a cylinder
  • Capacity of a half-cylinder
  • Conversion of units (cubic cm to litres)

Real-World Applications

  • Finding the capacity of a drinking trough or a container
  • Calculating the volume of a cylinder or a half-cylinder
  • Converting units of measurement

Further Reading

  • Volume of a cylinder: [insert link]
  • Radius of a cylinder: [insert link]
  • Capacity of a half-cylinder: [insert link]
  • Conversion of units: [insert link]

References

  • [insert reference 1]
  • [insert reference 2]
  • [insert reference 3]

Glossary

  • Capacity: the amount of liquid that a container can hold
  • Cylinder: a three-dimensional shape with two parallel and circular bases connected by a curved lateral surface
  • Half-cylinder: a three-dimensional shape with one circular base and a curved lateral surface
  • Radius: the distance from the center of a circle to any point on the circle
  • Volume: the amount of space inside a three-dimensional shape
    The Figure Shows a Drinking Trough in the Shape of a Half-Cylinder: Q&A ===========================================================

Introduction

In our previous article, we explored the concept of finding the capacity of a half-cylinder shaped drinking trough. We used the formula for the volume of a cylinder to find the volume of the full cylinder, and then multiplied it by 2 to account for the half-cylinder shape. In this article, we will answer some frequently asked questions related to the topic.

Q&A

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

A: The formula for the volume of a cylinder is V = πr^2h, where V is the volume, π is a constant approximately equal to 3.14, r is the radius of the cylinder, and h is the height of the cylinder.

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

A: To find the radius of a cylinder, you need to divide the diameter by 2. The formula for finding the radius is r = diameter / 2.

Q: What is the capacity of a half-cylinder?

A: The capacity of a half-cylinder is equal to the volume of the full cylinder multiplied by 2. The formula for finding the capacity of a half-cylinder is Capacity = 2V.

Q: How do I convert the capacity from cubic cm to litres?

A: To convert the capacity from cubic cm to litres, you need to divide the capacity by 1000. The formula for converting the capacity is Capacity (litres) = Capacity (cubic cm) / 1000.

Q: What are some real-world applications of finding the capacity of a half-cylinder?

A: Some real-world applications of finding the capacity of a half-cylinder include finding the capacity of a drinking trough or a container, calculating the volume of a cylinder or a half-cylinder, and converting units of measurement.

Q: What are some common mistakes to avoid when finding the capacity of a half-cylinder?

A: Some common mistakes to avoid when finding the capacity of a half-cylinder include:

  • Not using the correct formula for the volume of a cylinder
  • Not converting the capacity from cubic cm to litres
  • Not multiplying the volume of the full cylinder by 2 to find the capacity of the half-cylinder

Q: How can I practice finding the capacity of a half-cylinder?

A: You can practice finding the capacity of a half-cylinder by using online calculators or worksheets that provide problems and solutions. You can also try creating your own problems and solutions to practice your skills.

Conclusion

In this article, we have answered some frequently asked questions related to finding the capacity of a half-cylinder. We have covered topics such as the formula for the volume of a cylinder, finding the radius of a cylinder, and converting units of measurement. We hope that this article has been helpful in clarifying any doubts you may have had.

Additional Resources

  • Online calculators for finding the capacity of a half-cylinder: [insert link]
  • Worksheets for practicing finding the capacity of a half-cylinder: [insert link]
  • Videos on finding the capacity of a half-cylinder: [insert link]

Glossary

  • Capacity: the amount of liquid that a container can hold
  • Cylinder: a three-dimensional shape with two parallel and circular bases connected by a curved lateral surface
  • Half-cylinder: a three-dimensional shape with one circular base and a curved lateral surface
  • Radius: the distance from the center of a circle to any point on the circle
  • Volume: the amount of space inside a three-dimensional shape