Perimeter, Area and Volume Grades F to A. Hyperlinks! Counting Squares Area – working backwards Circles Volume of cuboids Sectors of circles Surface area.

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Presentation transcript:

Perimeter, Area and Volume Grades F to A

Hyperlinks! Counting Squares Area – working backwards Circles Volume of cuboids Sectors of circles Surface area Volume of prisms Volume and surface area of complex shapes Rectangles and Triangles Parallelograms and Trapeziums Compound Shapes

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Area and perimeter by counting and measuring How do I find the area and perimeter of a shape? Grade F

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

What are perimeter and area? Perimeter is the length around the outside of a shape. Area is the space inside a shape.

Example The rectangle has a perimeter of: The rectangle has a area of: =16cm 5×3=15cm² 5+5= 5+ Take note of the units!

Find the perimeter and area of this rectangle: Perimeter = Area = 20cm 24cm²

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Rectangles and Triangles Can I calculate the perimeter and area of a rectangle and triangle? Grade E

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

The formulae to remember:

Two examples: Example 1 Find the area and perimeter of this rectangle: Area = 8 × 6 Area = 48cm² Perimeter = Perimeter = 28cm Example 2 Find the area of this triangle: Area = 5 × 12 ÷ 2 Area = 60cm² ÷ 2 Area = 30cm² 6cm 8cm 5cm 13cm 12cm

Have a go at some: Question 1 Find the area of this triangle: Question 2 Find the perimeter and area of this rectangle: 10cm 11cm 8cm 7cm Answer: 35cm² Answer: Area = 88cm² Perimeter = 38cm

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Parallelograms and Trapeziums Can I calculate the area of a parallelogram and trapezium? Grade D

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

The formulae:

Two examples Example 1 Find the area of this parallelogram: Area = 7 × 5 Area = 35cm² Example 2 7cm 5cm6cm 5cm 4cm 8cm

Have a go at a couple of questions: Question 1 Find the area of this parallelogram: Question 2 Find the area of this trapezium: 12cm 8cm 10cm 7cm 9cm 11cm Answer: 96cm² Answer: 70cm²

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Circles Can I find the circumference and area of a circle? Grade C

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Names to do with circles you must remember: Radius Diameter Chord Tangent Circumference

Formulae you need to remember:

A couple of examples Example 1 Find the circumference and area of a circle with a diameter of 10cm to 1 dp. Circumference = π × 10 Circumference = 31.4cm Area = π × 5² Area = 78.5cm² Example 2 Find the circumference and area of a circle with a radius of 8cm to 1 dp. Circumference = π × 16 Circumference = 50.3cm Area = π × 8² Area = 201.1cm²

Some for you to try: Question 1 Find the circumference and area of this circle to 1 dp. Question 2 Find the circumference and area of a circular pond with a diameter of 3m to 1 dp. Circumference = 88.0cm Area = 615.8cm² Circumference = 9.4m Area = 7.1m² 14cm

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Area – Working Backwards Now you can find the area of shapes, can you find a length having been given the area?

Formulae Reminder:

Find the missing lengths: Area = 48cm² Area = 21cm² Area = 32cm²Area = 28cm² Area = 113.1cm² 8cm ?cm7cm ?cm 8cm 9cm ?cm Diameter = ? Height = ?Height = 4cm None of these are drawn to scale 6cm 4cm 5cm 12cm

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Compound Shapes Can I calculate the perimeter and area of a compound shape? Grade C

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

What is a compound shape? A compound shape is a shape that is made up of lots of different shapes. The key is to split the complex shape up into simpler shapes, find the areas of the simple shapes then add your areas together.

An example Find the area of this shape: Split it up! Area = = 72cm² 12cm 8cm 3cm Area = 8×5 = 40cm² Area = 8×4 = 32cm²

Another example Find the area of this shape: Split it up! Area = = 67.5cm² 3m 9m 6m Area = 9×6 = 54m²

A couple of questions: Question 1 Find the area of this shape: Question 2 Find the area of this shape: 10m 8m 6cm 12cm 3cm 5cm Answer: 66cm²Answer: 119.3m²

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Volume of Cuboids Can I calculate the volume of a cuboid? Grade C

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

How to calculate the volume of a cuboid:

An example: Find the volume of this cuboid: Volume = 3 × 5 × 4 Volume = 60cm³ 3cm 5cm 4cm Take note of the units!

Another example, working backwards: Find the height of this cuboid: 280cm³ = 10 × 7 × h h = 280 ÷ (10 × 7) h = 4cm 10cm 7cm Volume = 280cm³

Two questions to have a go at: Question 1 Find the volume of this cuboid: Question 2 The tank below contains exactly 100 litres of water. How far up the tank does the water go? (Hint: 1 litre = 1000cm³) 5cm 8cm 6cm 1m 0.5m Answer: 240cm³Answer: 0.2m or 20cm

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Prisms Can I calculate the volume of a prism? Grade C

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

What is a prism? A prism is a 3D shape that has the same cross- section all the way through. For example: Triangular PrismHexagonal PrismCylinder

Calculating the volume of a prism: Find the area of the cross-section then multiply by the length. Volume = Area of cross-section × length

Two examples Example 1 Example 2 If the volume of this prism is 360cm³ and it is 9cm long, what is the area of the cross- section? Area of cross-section = 360 ÷ 9 Area of cross-section = 40cm² 8cm 3cm

A couple of questions: Question 1 Find the volume of this triangular prism: Question 2 A circular pond contains 18,850 litres of water. It has a diameter of 4m. How deep is the pond if it is a cylinder? (1 litre = 1000cm³) 8cm 12cm 9cm Answer: 432cm³ Answer: 1.5m or 150cm

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Surface Area Can I calculate the surface area of a cuboid or a triangular prism? Grade C to B

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

What is surface area? The area of all the faces of a 3D shape added together. You could think of it like this: it is the exact amount of wrapping paper you would need to wrap your shape up with.

Find the surface area of this cuboid: Each face you can see has a face exactly the same opposite it. 2 × 4 × 10 = 80cm² 2 × 4 × 5 = 40cm² 2 × 5 × 10 = 100cm² Total surface area = 220cm² 4cm 10cm 5cm 4cm × 5cm = 20cm² 5cm × 10cm = 50cm² 4cm × 10cm = 40cm² There are two of each size of rectangle

Find the surface area of these two cuboids: Cuboid 1 Answer: 258cm² Cuboid 2 Answer: 192cm² 9cm 5cm 6cm 4cm 12cm 3cm

A Triangular Prism Example:

A Cylinder Example: Find the surface area of this cylinder: It’s two circles and a rectangle (whose length is the circumference of the circle): Surface area = 2 × π × 4² + 5 × π × 8 Surface area = 226.2cm² 4cm 5cm The two circlesThe rectangle

Find the surface area: Answer: 527.8cm² 12cm 8cm

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Sectors of Circles Can I find the area of a sector and its arc length? Grade B

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

What is a sector? A sector is a fraction of a circle – like a slice of cake or pizza. It’s point is the centre of the circle. The arc length is the curved part of the sector.

The formulae: Area of a whole circle Circumference of a whole circle Angle given for the sector

An example Find the area and arc length of this sector. Area: Area = 21.4cm² Arc Length: Arc Length = 44.1cm

A question for you: Find the area and perimeter of this sector. (Don’t forget the “straight bits” for the perimeter!) Area = 15.4cm² Perimeter = 15.7cm

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Volume and Surface Area of Complex Shapes Can I use the formulae to find surface area and volume of cones and spheres? Grade A

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.

Some formulae for you: These formulae are at the front of the paper!

And one more…

Cone Example: 5cm 12cm 13cm Circular base Curved surface area

Sphere Example: r = 6cm

Two questions Question 1 Find the volume and curved surface area of this cone: Question 2 Find the volume and curved surface area of this sphere: 6cm 8cm C.S.A. = 188.5cm² Volume = 301.6cm³ Surface area = 804.2cm² Volume = cm³

The frustum A frustum is a cone or pyramid that has had it’s top chopped off! Remember: the original cone/pyramid and the cone/pyramid that has been chopped off are similar, mean that the dimensions are in the same ratio.

Find the volume of the frustum: 3cm 6cm 5cm Double the radius, so double the height

Try this one: Find the volume of this frustum: 3cm 9cm 8cm Answer: 980.2cm³

Success Criteria: Where Are We Now? LevelLearning outcomes:RAG F2 I can find the perimeter and area on a shape by measuring or counting. E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation. D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms such as cones and spheres using the formulae.