Wentworth's Plane and Solid Geometry · Book V, Exs. 503–530 · Book 6: Book V: Regular Polygons and Circles
77. Computing with circles and regular polygons
Goal: Your student solves numerical problems on circumferences, circle areas, sectors, segments and regular polygons.
You'll need
- The book, open to these pages
- Pencil and paper
- A calculator
What's in the book
Pages 244–245: numerical exercises 503–530.
The lesson, step by step
Warm up
Ask: Give the formulas for the circumference and area of a circle.
Circles
Ex. 504. Find the circumference and the area of a circle whose diameter is 8 feet.
Ex. 523. The diameter of a bicycle wheel is 28 inches. How many revolutions does the wheel make in going 10 miles ?
Use π = 3.1416 as the book does. One mile is 5280 feet.
A bridge
Ex. 527. The span (chord) of a bridge in the form of a circular arc is 120 feet, and the highest point of the arch is 15 feet above the piers. Find the radius of the arc.
Hint: use the two-chord theorem with the diameter through the top of the arch.
More
Your student does four or five more from Ex. 503–528.
Wrap up
Check the answers together.
Answers to the book's problems
Ex. 503: 144π, about 452.39 sq in. Ex. 504: 8π, about 25.13 ft; 16π, about 50.27 sq ft. Ex. 505 and 506: the apothem is ½√(4R² − a²). Ex. 507: about 752.4 sq in. Ex. 508: about 10.35 in. Ex. 509: about 146.9 ft. Ex. 510: about 76,942 sq yd. Ex. 511: about $942.50 (side about 78.5 yd). Ex. 514: about 35.8 ft. Ex. 515: about 35.8°. Ex. 516: about 5.37 sq ft. Ex. 517: about 69.8 sq in. Ex. 518: 4 ft. Ex. 519: about 31.02 ft. Ex. 520: 15√2, about 21.21 ft; 15√3, about 25.98 ft. Ex. 521: about 2.46, 3.48, 4.26 and 4.92 in. Ex. 522: about 2311 sq ft. Ex. 523: about 7203. Ex. 524: about 3.18 ft. Ex. 526: 3100π, about 9739 sq ft. Ex. 527: 127.5 ft. Ex. 528: R²(√3 − ½π), about 0.161 R².
Worked out for this site from the scan. If a number in your copy differs, trust the book.