polyhedron with a base that is a polygon and identical parallel opposite face whose corresponding edges are joined by parallelograms.

3D shape with a circle base and an identical parallel opposite face. Cross sections made parallel to the base will be congruent to the base.

the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.

the amount of space occupied by a closed 3D shape.

Problem solving with perimeter, area and volume

Maths

Checking understanding of perimeter

Checking understanding of area

Multiplicative relationships in circles

Circumference of a circle

Area of a circle

Using the formula for the area of a circle

Area of composite shapes

Perimeter of composite shapes

Finding a length in composite shapes

Surface area of cuboids

Properties of prisms

Surface area of prisms

Surface area of cylinders

Volume of prisms

Volume of cylinders

In this unit, pupils have derived the formula for the circumference and area of a circle. In the future unit, this knowledge is combined with knowledge of fractions to find the arc length and area of a sector.

 In the prior unit, pupils learnt how to derive and use the formula for the area of a triangle and trapezium. In this unit, this knowledge is called upon to find the volume of different prisms and area of composite shapes.

In this unit pupils extend their knowledge of shapes by exploring the properties of circles and composite shapes before developing understanding of 3-D shapes including surface area and volume.

Perimeter, area and volume

A composite prism can be created by using two or more {{ }}.

A cube has a volume of 125 cm³. The edge length of the cube is {{ }} cm.

A cube has a volume of 64 cm³. The area of one face is {{ }} cm².

Which of these shapes have the largest volume?

The amount of ribbon to put around a cake.

The amount of silver to cover an earring.

A cylinder has a volume of $$300\pi\text{ cm}^3$$ and a length of $$3\text{ cm}$$. The surface area of the cylinder is {{ }} $$\pi\text{ cm}^2$$.

The perimeter of this composite rectilinear shape is {{ }} cm.

The area of this composite rectilinear shape is {{ }} cm².

the total area of all the surfaces of a closed 3D shape.

A triangular prism with an equilateral triangle base has {{ }} different shape faces.

Not enough information to calculate the volume.

A hexagonal prism has a cross-sectional area of 62 cm² and a length of 5 cm. What is the volume of the prism?

A cylinder has a volume of $$252\pi\text{ cm}^3$$ and an integer length. Which of these could be the radius?

Problem solving with perimeter, area and volume

Lesson outcome