Area and circumference of circles

The topic Area and circumference of circles appears under the 7th grade (U.S.) Math Mission and High school geometry Math Mission. This exercise practices the relationship between radius, diameter and circumference in the context of word problems.

Types of Problems

There are two types of problems in this exercise:

1. Find total area of object: This problem uses the area of a circle formula to solve a word problem. Users are asked to find the correct area of an object and insert this in the space provided.

   

   Find total area of object

1. Use the circumference: This problem uses the circumference of a circle formula to solve a word problem. The user is asked to find the correct circumference and use it to find a solution.

   

   Use the circumference

Strategies

Knowledge of the four basic circle constants is an advantage on this exercise. Some other formulas arise such as metric unit conversions and area of a rectangle.

1. The circle constants are radius, diameter (which is twice the radius), circumference (which is ${2 \pi r}$ or also ${\pi d}$) and the area formula (which is ${\pi r^2}$), though not needed on this exercise.
2. The circumference formula can be remembered with the mnemonic "Cherry pies are delicious."
3. The area formula can be remembered with the mnemonic "Apple pies are too."
4. All four circle constants can be listed with the acronym CARD.
5. Be careful on the area problem to use the appropriate formulas when more than one is needed.
6. For the Use the circumference problem there is a situation where you need to use the circumference to figure out the distance that a wheel has traveled. Knowledge of the unit conversions is sometimes necessary on this problem.

Real-life Applications

1. Area and perimeter are used in many jobs for architecture and interior design.
2. The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.
3. Architects use triangles when building bridges, roofs on houses, and other structures.