1 / 16

Shape and Space

Shape and Space. Circles. Let us define Circle. A ___________is a simple shape that is the set of all points in a plane that are at a given distance from a given point, the center.

tait
Download Presentation

Shape and Space

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Shape and Space Circles

  2. Let us define Circle • A ___________is a simple shape that is the set of all points in a plane that are at a given distance from a given point, the center. • A circle is a simple shape that is the set of all points in a plane that are at a given distance from a given point, the center.

  3. Radius is the distance from the center to the edge of a circle. Radius is half of the diameter

  4. Diameteris a segment that passes through the center and has its endpoints on the circle. The diameter is twice the length of the radius

  5. The value of π = 3.141592653589793238462643383279502884197169 39937510582097494459230781640628620899862803482 53421170679821480865132823066470938446095505822 31725359408128481117450284102701938521105559644 62294895493038196 (to 200 decimal places)! We use the symbol π because the number cannot be written exactly.

  6. In circles the AREA is equal to 3.14( ) times the radius (r) to the power of 2. Thus the formula looks like: A= r2 In circles the circumference is formula looks like: 2 r The circumference of a circle is the actual length around the circle which is equal to 360°. πis equal to 3.14.

  7. The circumference of a circle Use π = 3.14 to find the circumference of this circle. R = 4 C = 2πr 8 cm = 2 × 4 = 8π

  8. The circumference of a circle 9 m 4 cm 58 cm Use π = 3.14 to find the circumference of the following circles: C = 2πr C = 2πr = 2 × 2 = 2 × π × 9 = 4πcm = 18πm 24mm C = 2πr C = 2πr = 2 × 12 = 2 × π × 58 = 12πmm = 116πcm

  9. Formula for the area of a circle We can find the area of a circle using the formula Area of a circle = π×r×r or radius Area of a circle = πr2

  10. Area of a circle

  11. The circumference of a circle Use π = 3.14 to find the area of this circle. 4 cm A = πr2 = π × 4 × 4 = 16π cm2

  12. The area of a circle 2 cm 10 m 78 cm 23 mm Use π = 3.14 to find the area of the following circles: A = πr2 A = πr2 = π × 22 = π × 52 = 4π cm2 = 25π m2 A = πr2 A = πr2 = π × 232 = π × 392 = 529π mm2 = 1521π cm2

  13. Find the area of this shape Use π = 3.14 to find area of this shape. The area of this shape is made up of the area of a circle of diameter 12cmand the area of a rectangle of width 6cm and length 12cm. Area of circle = π × 62 12 cm 6 cm = 36π cm2 Area of rectangle = 6 ×12 = 78 cm2 Total area = 36π + 78

  14. Finding the radius given the circumference C = = 2π 12 6 π 2 × π Use π = 3.14 to find the radius of this circle. C = 2πr 12 cm How can we rearrange this to make r the subject of the formula? r = ?

  15. Find the perimeter of this shape Use π = 3.14 to find perimeter of this shape. The perimeter of this shape is made up of the circumference of a circle of diameter 13 cm and two lines of length 6 cm. 14 cm 6 cm Perimeter = 14 x 6 Circumference = 2πr

  16. Circumference problem The diameter of a bicycle wheel is 50 cm. How many complete rotations does it make over a distance of 1 km? Using C = 2πr and π = 3.14, The circumference of the wheel = π × 50 = 157cm 50 cm

More Related