Circumference, Area and Volume

Become familiar with methods used to calculate two-dimensional and three-dimensional objects.

Calculate Circumference, Area and Volume

Credit: Pixabay

Measurement calculations are important in daily life. Area calculations are needed in many activities, including planning a garden, determining how much paint to cover a surface, or purchasing new carpet. Calculating volume is important when purchasing fuel, estimating beverages for a birthday celebration, planning hydration for a long hike, or selecting an appropriate storage container. Apply these basic formulas to calculate circumference, area, and volume of simple geometric shapes commonly used in weights and measures applications. TIP: Express all dimensions in terms of the same unit - for example, in terms of meter. A computed area will then be in terms of the square of the dimensional unit used - for example, square meter (m²) - and a computed volume will be in terms of the cube of the dimensional unit used - for example, cubic meter (m³).

• Circumference of circle: 3.1416 × diameter
• Area of circle: 0.7854 × diameter × diameter
• Area of rectangle: length × width
• Capacity of rectangular bin: length × width × depth
• Volume of cylinder: 0.7854 × diameter × diameter × height
• Approximate capacity of a container having sloping sides: vertical height × one-half the sum of top area and bottom area

Basic Definitions

• Perimeter: The continuous line forming the boundary of a closed geometric figure.  

  

• Circumference: The distance around the edge of a circle (or any curvy shape). A type of perimeter.
• Diameter: Any straight-line segment between two points on the circumference of a circle that passes through the center of the circle. Twice the length of the radius of a circle.
• Area: The size of a surface. The amount of space inside the boundary of a flat shape or the surface of an object. Measured in square units.
• Volume: The measurement of the amount of space occupied inside the three-dimensional space. Measured in cubic units.
• Capacity: The maximum amount that an object can contain. Measured in cubic units.

Resources for Students and Teachers:

• A Slice of Math Functions for Pi Day (NIST). Happy Pi Day! Pi is the ratio of a circle’s circumference to its diameter. We can use pi to calculate a diameter. If the circumference of the Earth at the equator is 40,075 kilometers, which it is, then the diameter of the Earth is equal to the circumference divided by pi, which is approximately 12,756 kilometers.
• The NASA Pi Day Challenge (NASA). Pi is also used all the time by NASA scientists and engineers to explore other planets. In this challenge, you can solve some of the same problems NASA scientists and engineers do using pi!
• Pi Day Activities: High School (NASA). Use these Pi Day lesson plans, problem sets, and articles to get students in grades 9 through 12 learning about STEM. Lessons and projects are aligned to NGSS and Common Core Math standards. 

Navigate to more SI base unit information:

• SI Units
• Length – meter (m)
• Time – second (s)
• Amount of substance – mole (mole)
• Electric current – ampere (A)
• Temperature – kelvin (K)
• Luminous intensity – candela (cd)
• Mass – kilogram (kg)
• Area
• Volume
• Prefixes
• U.S. Metrication
• U.S. Metrication FAQs
• Metric Kitchen
• National Metric Week
• NEST-R (STEM Registry)
• NIST Educational Resources