Ray's New Practical Arithmetic · Arts. 251–252 · Unit 25: Mensuration
117. The circle: circumference and area
Goal: Your child finds a circle's circumference from its diameter (and back), and its area from its radius (and back), using 3.1416.
You'll need
- Paper and pencil, or a slate or small whiteboard
- A can or round jar, and a piece of string
What's in the book
Page 321 gives the circumference rule (Art. 251), and page 322 the converse with problems. Page 322 also gives the area of a circle (Art. 252) and its problems, which finish on page 323. Answers are printed.
The lesson, step by step
Warm-up
Wrap a string around a can, then lay the same string across the top again and again. It goes across a little more than 3 times.
Circumference
Multiply the diameter by 3.1416.
and back again:
Divide the circumference by 3.1416.
The diameter of a wheel is 4 ft.: what is its circumference?
4 × 3.1416 = 12.5664 ft., about 12 ft. 6.8 in.
Area
Multiply the square of the radius by 3.1416.
and back again:
Divide the area by 3.1416, and extract the square root of the quotient.
Guided practice
Do these together:
If the girth of a tree is 12 ft. 5 in., what is its diameter?
Find the area of a circle whose radius is 21 ft.
Independent practice and check
Your child works the remaining problems on pages 322–323. The horse-tethered-to-a-post problem is a favorite. The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.
Mental-math wrap-up
Using "about 3": a circle with diameter 10 has circumference about? A circle with radius 2 has area about?