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

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.

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?

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