LI - To be able to calculate the volume and surface area of 3D objects using formulae.

This week in maths we will examine 3D shapes and learn to work out volume and surface area.

Volume measures how much space a 3D object contains and surface area uses what we have learned about 2D area, but on all of the surfaces that make up the 3D object.

The video below helps to explain this in a really straightforward way.

Note down the formulae as you watch and pay attention to the examples. Note: You do not need to learn the information for spheres and cones (unless you find it very interesting).

https://www.youtube.com/watch?v=qJwecTgce6c

Once you have watched the video and feel confident about the information, you will have four tasks that you m=can complete to practise these skills. Only task 1 is essential, so if you are finding it difficult to make time, just do task 1.

Task 1 will allow you to practise the core formulae for volume and surface area

Task 2 will show that irregular prisms can still be worked with if the area of the irregular side is known and allow you to practise with circular shapes

Task 3 will encourage you to use the formula for volume to work out missing information

Task 4 will allow you to practise finding volume and surface area for compound 3D shapes

Answers follow each task.

Email stephen.digan@craiglockhart.edin.sch.uk with any questions about your work.

Task 1

This task is about using the formulae you learned from the video above and practising the steps carefully. Answers are provided at the end.

Find the volume & surface areaQ1.

Q2.

Find the volume & surface areaQ1.

Q2.

Find the volume & surface area

4cm

4cm

8cm

3cm

3cm

5cm

Q1.

Q2.

Find the volume & surface areaQ1.

Q2.

Find the volume & surface area

5cm

5cm

5cm4cm 10c

6cm

6cm

6cm5cm 8cm

6cm

4cm 5cm8cm

7cm

3cm 4cm10cm

Q1.

Q2.

Find the volume & surface areaQ1.

Q2.

Find the volume & surface area

5cm4cm

2cm

6cm10cm

6cm5cm

3cm

5cm7cm

Q1.

Q2.

Find the volume & surface areaQ1.

Q2.

Answers:

Cubes: (1) V – 125cm3 SA - 150cm2 (2) V – 64cm3 SA - 96cm2

Square ended cuboids: (1) V – 45cm3 SA - 78cm2 (2) V – 128cm3 SA - 160cm2

Cuboids: (1) V – 480cm3 SA - 376cm2 (2) V – 144cm3 SA - 192cm2

Equilateral triangular prism: (1) V – 100cm3 SA - 170cm2 (2) V – 120cm3 SA - 174cm2

Isosceles triangular prism: (1) V – 288m3 SA - 288m2 (2) V – 360m3 SA - 336m2

Parallelogram prism: (1) V – 192cm3 SA - 224cm2 (2) V – 210cm3 SA - 262cm2

Triangular prism: (1) V – 36m3 SA - 84m2 (2) V – 96m3 SA - 144cm2

Trapezium prism: (1) V – 160cm3 SA - 212cm2 (2) V – 140cm3 SA - 180cm2

Task 2

Section A

Calculate the volume of these prisms (note that the area of the cross section is already done)

Section B

Calculate the volume of these prisms

Section C

Calculate the volume of these prisms

Extension (Challenge);

Answers – Volume of prism

Section A

1. 250 cm3

2. 510 cm3

3. 252 cm3

4. 4725 cm3

5. 132 m3

6. 480 m3

7. 186.76 m3

8. 60.68 m3

Section B

1. 90000 cm3

2. 252000 cm3

3. 18 m3

4. 36 m3

5. 96 cm3

6. 540 mm3

Section C

1. 140 cm3

2. 720 m3

3. 168 m3

4. 684 m3

Extension (Challenge)

i) Pi = 3.14 ii) pi(used on calculator)

1. i) 9043.2 cm3 ii) 9047.787cm3

2. i) 1538.6 cm3 ii) 1539.340 cm3

3. i) 276.9 cm3 ii) 277.088 cm3

4. i) 2034.7 cm3 ii) 2035.752 cm3

5. i) 763.0 cm3 ii) 763.40 cm3

6. a) 611.6 cm3 b) 212.1 cm3

c) 1194.6 cm3

Task 3

Find the length of each of these shapes.

Answers

a. 22cmb. 14cm

19 cm2

Volume = 418 cm3

Volume = 224 cm3

Volume = 324 cm3

Volume = 168 cm3

Volume = 400 cm3

Volume = 270 cm3

Volume = 330 cm3

Volume = 255 cm3

a)b)

c)d)

e) f)

g)h)

16 cm2

9 cm2

12 cm2

5 cm2

30 cm2

22 cm2

17 cm2

________________________________________________________________________________

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lengthlength

length

length

lengthlength

lengthlength

c. 36cmd. 14cme. 80cmf. 9cmg. 15cmh. 15cm

Task 4

Find the surface area and volume of these compound 3D shapes.

Answers:

1. Surface area – 456cm2 Volume – 480cm3

2. Surface area – 408cm2 Volume – 280cm3

6cm

4cm

3cm

3cm

12cm

8cm10cm

2.5cm 2.5cm

2.5cm 2.5cm

2cm

2cm

4cm

6cm

10cm

2m

2m

2m

1m

1m

4m

8m

7m1m

1m

1.

2.

3.

3. Surface area – 268cm2 Volume – 252cm3