Publicité
Publicité

### Circle & sphere

1. Circles and sphere
2. Sphere & Hemisphere sphere • A 3-dimensional object shaped like a ball. • Every point on the surface is the same distance from the center. Hemisphere • half of a sphere
3. Surface area of spheres surface area = 4 π r2 • Example 1 If 'r' = 5 for a given sphere, and π = 3.14, then the surface area of the sphere is: surface area = 4 π r2 = 4 × 3.14 × 52 = 314
4. Volume of spheres Question 1: Calculate the volume of a sphere of radius 13 cm ? Solution: Given, r = 13 cm Volume of a sphere = (4/3)πr3 = (4/3) π (13 cm)3 = 9202.772 cm3 Volume = (4/3) × π × r3
5. Surface area of hemisphere Total surface area of a hemisphere: S = (2πr2) + (πr2) S = 3πr2 Curve area Circle Question 1: Find the radius of a hemisphere where the total surface area is 1846.32 cm Solution:The total surface area of the hemisphere = 1846.32 cm2 We know, total surface area of a hemisphere = 3 π r2 square units.
6. Answer Therefore, 3 π r2 = 1846.32 3 ( 3.14 ) r2 =1846.32 9.42 r2 = 1846.32 r2 = 1814.929.42 r2 = 192.67 Radius of the hemisphere, r = 14 cm
7. Volume of hemisphere • Volume of a hemisphere: V = (1/2)(4/3)πr3 = (2/3)πr3 • Example: Calculate the volume of the hemisphere with a radius of 3cm. Answer: Volume of Hemisphere: = (2/3)πr³ = 56.55 cm
8. SECTOR CIRCLES • The circle is the shape with the largest area for a given length of perimeter. • A circle is a plane figure bounded by one line, and such that all right lines drawn from a certain point within it to the bounding line, are equal. • The Bounding line is called circumference. c Center Center
9. Circumference C π = = 3.14 22 7
10. AREA π = = 3.14 22 7 • The AREA is the amount inside the shape. Example : Find the Area A = πr A = 3.14 x 3 = 28.26 cm 2 2 2 12cm x 6cm = 72cm 2 72cm + 28.26cm = 100.26cm2 2 2
11. Trigonometry: Arc Length and Radian Measure An arc of a circle is a “portion” of the circumference of the circle. The arc length is the length of its “portion” of the circumference.