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.
