Edexcel IGCSE Math A 4.10 3D shapes and volume

Use this 3D mensuration page to identify solids, count edges, calculate surface area or volume and handle compound solids with consistent units.

Exam points

Name common solids and count faces, edges or vertices from diagrams accurately.
Calculate surface area or volume of prisms, cylinders, cones, spheres and hemispheres.
Convert volume units or combine solids before using density, area or volume formulae.

Covered syllabus points

4.10.A Names of solids 4.10.B Faces, edges and vertices 4.10.C The surface area of simple shapes using the area 4.10.D The surface area of a cylinder 4.10.E The volume of prisms 4.10.F Between units of volume within the metric system

[Maximum number: 5]

(a)

Write down the mathematical name of this 3-D shape.

Figure for Question (a) — Edexcel IGCSE Math A Foundation

[ 1 ]

(b)

How many faces does this shape have?

[ 1 ]

(c)

How many vertices does this shape have?

Here is a different 3-D shape.

Figure for Question (c) — Edexcel IGCSE Math A Foundation

Marie makes a model of the shape.
She uses a length of wire to make each edge of the model.
Each edge of the model is 5 cm long.
Marie has 70 cm of wire.

[ 1 ]

(d)

What length of wire does she have left after making the model?
m

[ 2 ]

Working:
$70-8\times5=30$

Final answer:
$30\text{ cm}$

M1 for a correct subtraction method, which may be done in two parts. A1 for 30. Correct answer scores full marks unless from obvious incorrect working.

[Maximum number: 5]

The diagram shows a solid triangular prism ABCDEF.

Figure for Question 4.10 3D shapes and volume question 2 — Edexcel IGCSE Math A Foundation

Diagram NOT accurately drawn
$EF=8\text{ cm}$ , $DE=6\text{ cm}$ , $DF=10\text{ cm}$ and $BF=25\text{ cm}$ .
Angle $DEF=90^\circ$ .

(a)

Work out the volume of the prism. $\mathrm{cm}^{3}$

[ 2 ]

Volume of the prism:
$24\times25=600$

Final answer:
$600\text{ cm}^3$

M1 ft 24 from part (a) for multiplying by 25. A1 ft.

(b)

Work out the total surface area of the prism.
$\mathrm{cm}^{2}$

[ 3 ]

Areas of faces:
$2\times24=48$ $8\times25=200,\quad 6\times25=150,\quad 10\times25=250$ 48+200+150+250=648

Final answer:
$648\text{ cm}^2$

M2 for a complete method; if not M2, award M1 for at least 3 correct areas. A1.

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Covered syllabus points

4.10 3D shapes and volume question 1

Question (a)

Question (b)

Question (c)

Question (d)

4.10 3D shapes and volume question 2

Question (a)

Question (b)