Y9 – Autumn – Block 4 – Step 1 – Know names of 2D and 3D shapes Answers

Question Answer

1

2

3

4

cone triangle rectangle

sphere tetrahedron

square-based pyramid

cylinder

cuboid

parallelogram

isosceles triangle

decagon

pentagon

triangular prism

cube

cylinder

sphere

right-angled trapezium

kite

rhombus

Y9 – Autumn – Block 4 – Step 1 – Know names of 2D and 3D shapes Answers (continued)

Question Answer

5

a)

b) multiple possible answers, e.g.:

Students are likely to have drawn different pentagons.

6

a)

b) All students should be familiar with the cube and the tetrahedron. Some of the others may be unfamiliar.

c) They are all regular polygons.

✔ ✔

✔

Y9 – Autumn – Block 4 – Step 2 – Recognise prisms (including language of edges/vertices) Answers

Question Answer

1

2

3

a) It has a constant cross-section.b) The cross-section is not a polygon.A cylinder is not a prism, as all the faces of a prism must be polygons.

4

✔ ✔

triangular prism

tetrahedron hemisphere

cuboid

✔ ✔

Y9 – Autumn – Block 4 – Step 2 – Recognise prisms (including language of edges/vertices) Answers (continued)

Question Answer

5

6

7

a)

b)

8

! − # + % is always 2

parallelogram

equilateral triangle

hexagon

6

5

8

10

8

6

12

16

12

9

18

24

2

2

2

2

Y9 – Autumn – Block 4 – Step 3 – Accurate nets of cuboids and other 3D shapes Answers

Question Answer

1

multiple possible answers, e.g.:

All nets should have a square on either side of the line of four squares, but the positions of the two squares may differ.

2

multiple possible answers, e.g.:

All students should have the same six rectangles, but they may be arranged differently.

Y9 – Autumn – Block 4 – Step 3 – Accurate nets of cuboids and other 3D shapes Answers (continued)

Question Answer

3

multiple possible answers, e.g.:

4

multiple possible answers, e.g.:

Y9 – Autumn – Block 4 – Step 4 – Sketch and recognise nets of cuboids and other 3D shapes Answers

Question Answer

1

2

multiple possible answers, e.g.:

All nets should have six squares, but the arrangement may be different.

3

4

multiple possible answers, e.g.:

✔

✔

Y9 – Autumn – Block 4 – Step 4 – Sketch and recognise nets of cuboids and other 3D shapes Answers (continued)

Question Answer

5

a) coneb) tetrahedronc) pentagonal-based pyramidd) triangular prism

6

The pairs of sides adding up to 7 must be as shown here, but which pair of numbers is put on which pair of faces may differ.a)

b)

7

8

5

4

6

32

1

32

1

5

64

✔

✔

Y9 – Autumn – Block 4 – Step 5 – Plans and elevations Answers

Question Answer

1

2

a)

b) \

The square would be at the other end of the rectangle.

3

✔

Y9 – Autumn – Block 4 – Step 5 – Plans and elevations Answers (continued)

Question Answer

4

a)

b)

5

a)

b)

Y9 – Autumn – Block 4 – Step 6 – Find area of 2D shapes Answers

Question Answer

1

a) 15 cm2

b) 16 cm2

c) 54 cm2

d) 40 mm2

2 ℎ = 4 cm

3a) 25 cm2

b) 10 m2

4

a) 43 m2

b) 184 cm2

c) 84 cm2

d) 119.5 m2

5

a) 0.16π cm2

b) 36π km2

c) 8π cm2

d) 20.25π mm2

Y9 – Autumn – Block 4 – Step 7 – Surface area of cubes and cuboids Answers

Question Answer

1a) 9 cm2

b) 54 cm2

2

a) 150 cm2

Each face has area 25 cm2. There are six faces, so total area = 150 cm2

b) 7 m

3

a) " = 30 cm, # = 20 cm, $ = 6 cmb)

c)

d) 1,800 cm2

4a) He has only counted one of each size of rectangle. There are two rectangles of each size.b) 108 cm2

5

BA has surface area 1,350 cm2

B has surface area 1,800 cm2

6 £391.50

7 % = 2.5 cm

8 6"2 + 48"

back

top

bottom

sideB

sideA

600 600 120 120 180 180

Y9 – Autumn – Block 4 – Step 8 – Surface area of triangular prisms Answers

Question Answer

1

a)

b) 184 cm2

2Amir has assumed that the sides of the triangle are all the same, and so that the rectangular faces are all the same size.

3 264 cm2

4 1,768 cm2

5

a) accurate drawing of equilateral triangle with side length of 3.6 cmb) 3.1 cmc) 49.0 cm2 (to 3 significant figures)

6 75%

7 7.5 m

50

60

50

12

12

Y9 – Autumn – Block 4 – Step 9 – Surface area of a cylinder Answers

Question Answer

1

a) 28.3 cm2

b) 18.8 cmc) 150.8 cm2

d) 207.3 cm2

2

a)

b) 361 cm2

3 88π cm2

4

surface area of A = 281.5 cm2

surface area of B = 279.6 cm2

B

5

diameter = 2ℎ so radius = ℎarea of circle = πℎ2area of curved surface = ℎ × 2πℎ = 2πℎ2total surface area = 2πℎ2 + 2 × πℎ2 = 4πℎ2

6a) 725.7 cm2

b) 8.1 m2

Y9 – Autumn – Block 4 – Step 10 – Volume of cubes and cuboids Answers

Question Answer

1

a) 125 cm3

b) 616 cm3

c) 1,725 mm3

d) 10.26 m3

2

No.The front face is a square, so all the sides are 4 cm.The volume is 448 cm3

3

a) ! = 5 cmb) # = 2.5 cmc) $ = 5 cm

4

a) 6 cmb) length of side = ! 1,000,000 = 100 mm

surface area = 6 × 1002 = 60,000 mm2

5 12.5 cm

6

a) 500 m3

b) 702 cm3

Work out the cross-section of the prism and multiply by the length.

7a) 8!3b) 2!2(! + 10) = 2!3 + 20!2

Y9 – Autumn – Block 4 – Step 11 – Volume of other 3D shapes – prisms and cylinders Answers

Question Answer

1

a) 240 cm3

b) 105 cm3

c) 202.5 mm3

2a) 2.41 m3

b) 27,000π mm3

3a) " = 5.6 cmb) $ = 2.1 cm

4 289 m3

5a) 4,095 cm3

b) 44,740 mm3

6 " = 8.5 cm

7

volume of A = 27"3volume of B = 16"3volume of C = 12"3A

Y9 – Autumn – Block 4 – Step 12 – Explore volumes of cones, pyramids and spheres Answers

Question Answer

1a) 314 cm3

b) 188 cm3

2a) 1,560 cm3

b) 1,290,000 mm3

3a) 112

3 cm3

b) 25 m3

4 782 cm3 (to 3 significant figures)

5 5.5 cm

6

football

radius = ! 3 ×5,6004" = 11 cm, so diameter = 22 cm

A football is more likely to have a diameter of 22 cm.

7 23.5 mm

8a) 0.372π m3

b) 27,600π mm3

9

volume = 13× 2302 × 147 = 2,592,100 m3

This is 2.6 millions metres cubed to 2 significant figures, so the information on the website seems to be accurate.

10

They all have a base of area 36 cm2 and height of 10 cm, so they all have the same volume.The first two pyramids have a square base and the third pyramid has a rectangular base.The first and third pyramids have the apex above the centre of the base, and the second pyramid has the apex not above the centre of the base.