Introduction to Circle and Half Circle A circle is defined as the locus of all points which moves in a plane such that its distance from fixed point in a plane is always a constant. The fixed point is known the centre and the constant distance is called the radius of circle. The straight line which passes through the centre and touches periphery two times is known as diameter. Diameter (d) = 2 Radius (r) Circle Half Circle If we divide the circle into two parts along the diameter the figure we get is known as half or semi circle. When we cut any part along radius which makes any angle with the center is known as sector of circle, half circle is sector of circle which makes 90o on the center. Formula of Circle Complete Circle Half Circle Circle Segment make '?' on the Center Area `pi r^2` `(pi(r)^2)/(2)` `(pi(r)^2 theta)/(360^o)` Periphery `2 pi r` `pi r` `(pi r theta)/(360^o)` Examples of Half Circle Ex 1 : Find area of half circle whose diameter is 12 cm. Sol: Step 1: Diameter of half circle (d) =12 cm Radius of half circle (r) = `(d)/(2)` = `(12)/(2)` = 6 cm Step 2:Area of half circle = `(pi r^2)/(2)` = `pi 6^2/2` = 56.54866 cm2 Ans Ex 2 : Find the periphery of arc whose radius is 5cm and making a sector angle 60o on the center ? Sol : Step 1:We know the formula Periphery = `(2pi r (theta) )/(360^o)` Step 2:Given values are r = 5 cm and `theta = 60^o` Step 3: Plug in the values in the formula Periphery = `(2pi (5) (60^o) )/(360^o)` = `(2pi (5) )/(6^o)` = 5.2359 cm Exercise Problems on Half Circle Formuls: 1) Find the area of half circle with radius 5 cm? Ans : 39.26 cm 2) Find the diameter of half circle whose periphery is 5p cm? Ans: 10 cm Know more Find the Center of a Circle i found this interesting link Central Angle of a Circle
Related Articles -
Half, Circle,
|