Slide 1: How would you calculate the area of this circle ? ...probably using the formula A = R2 Since the diameter is 2 feet, Click your mouse for the next idea ! The constant , called “pi”, is about 3.14 ?
Slide 2: Click your mouse for the next idea ! ? LETS explore how people figured out circle areas before all this business ? The ancient Egyptians had a fascinating method that produces answers remarkably close to the formula using pi.
Slide 3: Click your mouse for the next idea ! ? The Egyptian Octagon Method Draw a square around the circle just touching it at four points. What is the AREA of this square ? 2 feet Well.... it measures 2 by 2,
so the
area = 4 square feet.
Slide 4: Click your mouse for the next idea ! The Egyptian Octagon Method 2 feet Now we divide the square into nine equal smaller squares.
Sort of like a tic-tac-toe game ! Notice that each small square is 1/9 the area of the large one -- we’ll use that fact later !
Slide 5: Click your mouse for the next idea ! The Egyptian Octagon Method 2 feet Finally... we draw lines to divide the small squares in the corners in half, cutting them on their diagonals. Notice the 8-sided shape, an octagon, we have created ! Notice, also, that its area looks pretty close to that of our circle !
Slide 6: Click your mouse for the next idea ! The Egyptian Octagon Method 2 feet The EGYPTIANS were very handy at finding the area of this Octagon
Slide 7: Click your mouse for the next idea ! The Egyptian Octagon Method 2 feet ...and ALTOGETHER we’ve got... For a total area that is 7/9ths of our original big square
Slide 8: Click your mouse for the next idea ! The Egyptian Octagon Method 2 feet FINALLY... Yep, we’re almost done ! The original square had an area of 4 square feet. So the OCTAGON’s area must be 7/9 x 4 or 28/9 or 3 and 1/9 or about 3.11 square feet
Slide 9: AMAZINGLY CLOSE
to the pi-based “modern” calculation for the circle ! 3.11 square feet 3.14 square feet only about 0.03 off... about a 1% error !!
Use the Formula : Use the Formula A = r2
Area = pi times radius squared
Example : Example 8 mm A = r2 A = 3.14 x (82) A =3.14 x 64 A = 200.96 mm2
Example 2 : Example 2 13 cm If you are given a diameter, divide it in half to find the radius. 13 divided by 2 equals 6.5 cm. A = r2 A = 3.14 x (6.52) A = 3.14 x 42.25 A = 132.665 cm2
Slide 13: Find the area of the circle. Formula: A = π r² r=4cm A=3.14 x (4cm)² A=3.14 x 16cm² A= 50.24cm²
Slide 14: Area of a Circle Formula: A = π r² r=6cm A=3.14 x (6cm)² A=3.14 x 36cm² A= 113.04cm²
Slide 15: Area of a Circle Formula: A = π r² r=2.5m A=3.14 x (2.5m)² A=3.14 x 6.25m² A= 19.625m²
Slide 16: Find the area of the circle. Formula: A = π r² d=6cm A=3.14 x (3cm)² A=3.14 x 9cm² A= 28.26cm² R = 6cm ÷ 2 = 3cm
Slide 17: Find the area of the circle. Formula: A = π r² d=14cm A=3.14 x (7cm)² A=3.14 x 49cm² A= 153.86cm² R = 14cm ÷ 2 = 7cm