Capsule Calculator

Concepts

A capsule calculator is a tool that is used to calculate the volume and surface area of a capsule. A capsule is a geometric shape that is similar to a cylinder with rounded ends. It is also known as a stadium of revolution.

Volume of a capsule

The volume of a capsule is calculated using the following formula:

Volume = π * r^2 * h

Where:

  • π is a mathematical constant with the approximate value of 3.14
  • r is the radius of the capsule
  • h is the height of the capsule

Surface area of a capsule

The surface area of a capsule is calculated using the following formula:

Surface area = 2π * r * h + 2π * r^2

Where:

  • π is a mathematical constant with the approximate value of 3.14
  • r is the radius of the capsule
  • h is the height of the capsule

Formulae

The following table shows the formulae for calculating the volume and surface area of a capsule:

PropertyFormula
VolumeV = π * r^2 * h
Surface areaS = 2π * r * h + 2π * r^2

Benefits

There are several benefits to using a capsule calculator:

  • It can help you to quickly and easily calculate the volume and surface area of a capsule.
  • It can be useful for engineers, scientists, and other professionals who need to work with capsules.
  • It can also be used by students to learn about the volume and surface area of capsules.

Interesting facts

  • Capsules are used in a variety of applications, including:
    • Medicine: Capsules are used to deliver medication to patients.
    • Food and beverage: Capsules are used to encapsulate food and beverage products, such as spices and flavorings.
    • Cosmetics: Capsules are used to encapsulate cosmetic products, such as lipstick and blush.
    • Industrial products: Capsules are used to encapsulate industrial products, such as lubricants and adhesives.

References

  • Engineering Mechanics: Statics and Dynamics by R. C. Hibbeler (2017)
  • Mechanics of Materials by James M. Gere (2012)
  • Calculus: Early Transcendentals by James Stewart (2018)

Examples

The following table shows some examples of capsule calculations:

Radius (r)Height (h)VolumeSurface area
1 cm2 cm3.14 cm^310.18 cm^2
2 cm3 cm12.56 cm^322.68 cm^2
3 cm4 cm28.27 cm^335.18 cm^2

Applications

Capsule calculators can be used in a variety of applications, including:

  • Engineering: Engineers use capsule calculators to design and operate machines and equipment that use capsules.
  • Science: Scientists use capsule calculators to study the properties of capsules and to develop new applications for capsules.
  • Education: Students use capsule calculators to learn about the volume and surface area of capsules and to solve practice problems.

Conclusion

Capsule calculators are a valuable tool for anyone who needs to work with capsules. They can help you to quickly and easily calculate the volume and surface area of capsules.

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