Problem solving with perimeter, area and volume | Maths

Starter quiz

The perimeter of this composite rectilinear shape is ______ cm.

'148' ✓
The area of this composite rectilinear shape is ______ cm².

'852' ✓
Match each word to its definition.

Area

⇔

the size of the surface. ✓

Perimeter

⇔

the distance around a 2D shape. ✓

Volume

⇔

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

Surface area

⇔

the total area of all the surfaces of a closed 3D shape. ✓
A triangular prism with an equilateral triangle base has ______ different shape faces.

'2' ✓
A hexagonal prism has a cross-sectional area of 62 cm² and a length of 5 cm. What is the volume of the prism?

$67\text{ cm}^3$

$310\text{ cm}^3$ ✓

$620\text{ cm}^3$

Not enough information to calculate the volume.
A cylinder has a volume of $252\pi\text{ cm}^3$ and an integer length. Which of these could be the radius?

2 cm ✓

3 cm ✓

4 cm

6 cm ✓

9 cm

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

'prisms' ✓
A cube has a volume of 125 cm³. The edge length of the cube is ______ cm.

'5' ✓
A cube has a volume of 64 cm³. The area of one face is ______ cm².

'16' ✓
Which of these shapes have the largest volume?

Shape a ✓

Shape b

They both have the same volume
Match the measurement to the context.

Length

⇔

The amount of ribbon to put around a cake. ✓

Area

⇔

The amount of carpet to cover a floor. ✓

Surface area

⇔

The amount of silver to cover an earring. ✓

Volume

⇔

The amount of soil to fill in a hole. ✓
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 ______ $\pi\text{ cm}^2$ .

'260' ✓

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The volume and surface area of shapes made from prisms and cylinders can be found.
The volume and surface area of shapes made from parts of prisms and cylinders can be found.
Unknown lengths can be found when surface area or volume are known.
Volume and surface area can be used in context to solve problems.

Pupils may struggle to decide whether the question is needing length, area or volume.

Support could be given by providing the units for the answer or pupils may be encouraged to think of contexts for each before hand.

Prism - polyhedron with a base that is a polygon and identical parallel opposite face whose corresponding edges are joined by parallelograms.
Cylinder - 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.
Surface area - the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.
Volume - the amount of space occupied by a closed 3D shape.