Starter Find the Perimeter and Area of this shape… 12m 15m Perimeter 15m + 15m + 12m = 42m C = πd C = π x 12 C = 37.70m (2dp) Semi circle so… ÷ 2 = 18.85m In total… 42m m = 60.85m Area Whole Rectangle, subtract the semi-circle Rectangle 12m x 15m = 180m 2 Semi Circle A = πr 2 A = π x 6 2 A = m ÷ 2 = 56.55m 2 180m m 2 = m 2

Length of an Arc and Area of a Sector Last lesson we looked at finding the Area and Perimeter (Circumference) of circles We also looked at a number of problems involving semi circles and compound shapes This lesson we will be looking at ways of solving a problem involving a sector of a circle, and the length of an arc Arc Sector

Length of an Arc and Area of a Sector Length of an Arc πd x angle at centre 360 Area of a Sector πr 2 x angle at centre 360

Length of an Arc and Area of a Sector Find the Arc length and Area of the following sector 3cm 100º Arc length Find the circumference, and then multiply by the fraction of the circle C = πd C = π x 6 C = 18.85… For the Arc x 100 / 360  5.24cm (2dp) Area of Sector Find the total area, and then multiply by the fraction of the circle A = πr 2 A = π x 3 2 A = 28.27… For the Sector x 100 / 360  7.85cm 2 (2dp)

Length of an Arc and Area of a Sector Find the Arc length and Area of the following sector 8m 41º Arc length Find the circumference, and then multiply by the fraction of the circle C = πd C = π x 16 C = 50.27… For the Arc x 41 / 360  5.72m (2dp) Area of Sector Find the total area, and then multiply by the fraction of the circle A = πr 2 A = π x 8 2 A = … For the Sector x 41 / 360  22.90m 2 (2dp)

Length of an Arc and Area of a Sector Finding the Angle Work out the angle indicated using the information you are given 9cm25cm Imagine the formula to begin with… Arc = πd x 25 = π x 18 x 25 = 9000 = 18πa = a a 360 angle πa 360 Multiply by 360 Divide by 18π

Length of an Arc and Area of a Sector Finding the Angle Work out the angle indicated using the information you are given 2m Imagine the formula to begin with… Arc = πd x 2 = π x 4 x 2 = 720 = 4πa 57.3 = a a 360 angle 360 4πa 360 Multiply by 360 Divide by 4π

Length of an Arc and Area of a Sector Finding the Diameter Work out the length indicated using the information you are given 25m 105º Imagine the formula to begin with… Arc = πd x 25 = π x d x 25 = 9000 = 105πd = d angle πd 360 Multiply by 360 Divide by 105π

Length of an Arc and Area of a Sector Finding the Diameter Work out the diameter using the information you are given 32cm 205º Imagine the formula to begin with… Arc = πd x 32 = π x d x 32 = = 205πd = d angle πd 360 Multiply by 360 Divide by 205π

Length of an Arc and Area of a Sector Finding the Radius Work out the radius of this sector.. 35cm 2 160º Imagine the formula to begin with… Area = πr 2 x 35 = π x r 2 x 35 = = 160πr = r angle πr Multiply by 360 Divide by 160π r = 5.01cm √

Plenary πd x angle 360 π x 80 x = (2dp) = (2dp) ÷ 3= 38.3 rolls = 39 rolls Add 80m (the radii)

Summary We have learnt how to find the Length of an Arc, and the Area of a Sector We have also looked at solving ‘reverse’ problems, and finding the radius and angle We have again looked at some other questions where only a certain area is required