Geometric Shape Calculations and Sector Analysis
This content covers calculations for the area and circumference of various shapes, including circles and sectors. It provides step-by-step solutions with visual aids for better understanding. You will learn how to calculate areas, perimeters, arc lengths, and more using given dimensions and percentages of whole circle areas.
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Starter Calculate the area and circumference (or perimeter) of the following shapes. Give your answers correct to 3 significant figures. A = 38.5 cm C = 22.0 cm A = 56.5 cm C = 30.8 cm A = 9.42 cm C = 13.4 cm
Calculate the area and circumference of the circles with the following dimensions: A = r = x 2.5 = _____cm C = d = x 5 = _____cm A = r = x 4 = _____cm C = d = x 8 = _____cm A = r = x 1.5 = _____cm C = d = x 3 = _____cm A = r = x __ = _____cm C = d = x __ = _____cm
How would you calculate the area of this sector? 6 cm of the area of the whole circle
How would you calculate the area of this sector? 8 cm 60 1/6 of the area of the whole circle
How would you calculate the area of this sector? 53 4 cm 53 of the area of the whole circle 360
Calculate the area of this sector and the length of its arc. A = 53 x x 4 360 = 7.40 cm 53 L = 53 x x 8 360 = 3.70 cm 4 cm
Calculate the area of this sector and the length of its arc. A = 237 x x 6.2 360 = 79.46 m 6.2 m 237 L = 237 x x 12.4 360 = 25.65 m
r Area of sector = _ _ x x r 360 Length of arc = _ _ x x d 360
Checkpoint: Calculate the area of this sector and the length of its arc. A = 26 x x 6.5 360 = 9.59 m 26 L = 26 x x 13 360 = 2.95 m 6.5 m
Extension The diagram shows a pond. The pond is in the shape of a sector of a circle. Toby is going to put edging on the perimeter of the pond. Edging is sold in lengths of 1.75 metres. Each length of edging costs 3.49. Work out the total cost of edging Toby needs to buy.
Answers 1a) 16.8cm b) 62.8cm c) 219.9mm 2a) 47.5cm b) 463.6mm c) 589.0cm
The length of the arc on this sector is 12.54 cm. Calculate the angle at the centre. L = _ x x d 360 2.54 = _ x x 6.4 360 0.396 = _ x 360 0.126 = _ 360 45.5 = 2.54 cm 3.2 cm
The area of this sector is 78.6 mm. Calculate the angle at the centre. A = _ x x r 360 78.6 = _ x x 7 360 1.604 = _ x 360 0.510 = _ 360 183.8 = 7 mm 28.6 mm
Extension The diagram shows a pond. The pond is in the shape of a sector of a circle. Toby is going to put edging on the perimeter of the pond. Edging is sold in lengths of 1.75 metres. Each length of edging costs 3.49. Work out the total cost of edging Toby needs to buy.
Answers 3a) 60 b) 140 c) 280 4a) 70 b) 145 c) 320 Extension Answer: 20.94
