Starter quiz
- Find the positive value of that is a solution to the equation: . ______.
- '9' ✓
- Select the fully factorised form of this expression: .
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- ✓
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- Find the positive value of that is a solution to the equation: . ______
- '2' ✓
- Select the fully factorised form of this expression: .
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- A circle has a radius of 1.2 cm. Find the area of this circle. Give your answer in cm, rounded to 2 decimal places. Area = ______ cm².
- '4.52' ✓
- The area of a circle is 908 cm². Use the formula: to form an equation and solve this equation to find the radius of the circle, rounded to the nearest integer. ______ cm.
- '17' ✓
Exit quiz
- A quarter-circular sector is cut out of a circle. The quarter-circle has an area of 32 cm². What was the area of the original circle?
- 8 cm²
- 128 cm² ✓
- 402.12 cm²
- 16384 cm²
- 402.12 cm² ✓
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- A semi-circular sector is cut out of a circle. The semicircle has an area of 98 cm². Which of these statements are true about the original circle?
- The original circle has an area of 49 cm².
- The original circle has an area of 196 cm². ✓
- The original circle has a radius of 7 cm.
- The original circle has a radius of 14 cm. ✓
- The original circle has a diameter of 14 cm.
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- This composite shape is composed of a quarter-circle and a square. The area of the composite shape is 114 cm². Which of these statements about the shape are correct?
- Area of the square is
- Area of the square is ✓
- Area of the quarter-circle is ✓
- Area of the whole shape is ✓
- Area of the whole shape is
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- This composite shape is composed of a quarter-circle and a square. The area of the composite shape is 216 cm². Which of these equations are correct steps in the method to find the radius?
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- The area of this composite shape is: () cm². Find the value of . ______.
- '128' ✓
- This composite shape is composed of two quarter-circles and a square. The area of this composite shape is 1360 cm². Find the value of , rounded to the nearest integer. ______
- '23' ✓
Worksheet
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Presentation
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Lesson Details
Key learning points
- The diameter can be found from the area of circles or parts of circles by rearranging the formula.
- The radius can be found from the area of circles or parts of circles.
- The diameter or radius can be found from the area of composite shapes by reasoning and rearranging the formula.
Common misconception
If I want to find the radius of a semicircle from its area, I half the area first.
You must double the area. This calculates the area of a full circle, whose radius can be found by first dividing by π, then square rooting.
Keywords
Sector - A sector is the region formed between two radii and their connecting arc.
Diameter - The diameter of a circle is any line segment that starts and ends on the edge of the circle and passes through the centre of the circle.
Radius - The radius is any line segment that joins the centre of a circle to its edge.
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