Year 6 Maths reasoning (SATs): 3-D shapes, circles and angle types
Part of the Year 6 Maths reasoning (SATs) geometry: angles and shapes chapter. Chapter overview · whole chapter on one page
3-D shapes, circles and angle types
Rule
A face is a flat surface, an edge is where two faces meet, and a vertex is a corner.
In a circle, the radius goes from the centre to the edge, and the diameter goes across the whole circle through the centre. Diameter = 2 x radius.
Acute: less than 90 degrees. Right: 90. Obtuse: between 90 and 180. Reflex: more than 180 and less than 360.
Key ideas
- Diameter = 2 x radius.
- Acute < 90; obtuse between 90 and 180; reflex between 180 and 360.
- A cube has 6 faces, 12 edges and 8 vertices.
Method. Count the edges: the lines where two faces meet.
- Picture the shape. A cube has 6 faces, 12 edges and 8 vertices.faces 6, edges 12, vertices 8
- Count the edges. An edge is where two faces meet.12 edges
- Write the answer. 12
Check. 6 faces + 8 vertices - 12 edges = 2. ✓
Watch out. Edges are not faces. A cube has 12 edges, not 6.
Method. Use diameter = 2 x radius.
- Write the rule. Diameter = 2 x radius.2 x 5
- Multiply. Double the radius.10
- Write the answer. 10
Check. diameter = 2 x radius, so 20 = 2 x 10 or 5. ✓
Watch out. The radius is half the diameter. Do not double it when you need the radius.
Method. Compare the size with 90 and 180 degrees.
- Compare with 90 and 180. 250 degrees is compared with the rules for each type.250 is between 180 and 360 degrees
- Name the angle. An angle that is between 180 and 360 degrees is reflex.reflex
- Write the answer. reflex
Check. 250 is between 180 and 360 degrees. ✓
Watch out. An angle of exactly 180 degrees is a straight line; more than 180 is reflex.
Watch out
Watch out. The radius is half the diameter, not twice it. A diameter of 10 cm has a radius of 5 cm.
Exam tip
Practice guide. Count the faces, edges and vertices of a solid from a labelled picture before you answer.
Exercise 5E Practice: 3-D shapes, circles and angle types
Non-calculatorMethod. Count the edges: the lines where two faces meet.
- Picture the shape. A triangular prism has 5 faces, 9 edges and 6 vertices.faces 5, edges 9, vertices 6
- Count the edges. An edge is where two faces meet.9 edges
- Write the answer. 9
Check. 5 faces + 6 vertices - 9 edges = 2. ✓
Watch out. Edges are not faces. A cube has 12 edges, not 6.
Method. Count the edges: the lines where two faces meet.
- Picture the shape. A square-based pyramid has 5 faces, 8 edges and 5 vertices.faces 5, edges 8, vertices 5
- Count the edges. An edge is where two faces meet.8 edges
- Write the answer. 8
Check. 5 faces + 5 vertices - 8 edges = 2. ✓
Watch out. Edges are not faces. A cube has 12 edges, not 6.
Method. Count the edges: the lines where two faces meet.
- Picture the shape. A cuboid has 6 faces, 12 edges and 8 vertices.faces 6, edges 12, vertices 8
- Count the edges. An edge is where two faces meet.12 edges
- Write the answer. 12
Check. 6 faces + 8 vertices - 12 edges = 2. ✓
Watch out. Edges are not faces. A cube has 12 edges, not 6.
Method. Use diameter = 2 x radius.
- Write the rule. Radius = diameter / 2.14 / 2
- Divide. The radius is half the diameter.7
- Write the answer. 7
Check. diameter = 2 x radius, so 14 = 2 x 7 or 14. ✓
Watch out. The radius is half the diameter. Do not double it when you need the radius.
Method. Use diameter = 2 x radius.
- Write the rule. Diameter = 2 x radius.2 x 7
- Multiply. Double the radius.14
- Write the answer. 14
Check. diameter = 2 x radius, so 28 = 2 x 14 or 7. ✓
Watch out. The radius is half the diameter. Do not double it when you need the radius.
Method. Compare the size with 90 and 180 degrees.
- Compare with 90 and 180. 40 degrees is compared with the rules for each type.40 is less than 90 degrees
- Name the angle. An angle that is less than 90 degrees is acute.acute
- Write the answer. acute
Check. 40 is less than 90 degrees. ✓
Watch out. An angle of exactly 180 degrees is a straight line; more than 180 is reflex.
Method. Compare the size with 90 and 180 degrees.
- Compare with 90 and 180. 90 degrees is compared with the rules for each type.90 is exactly 90 degrees
- Name the angle. An angle that is exactly 90 degrees is right.right
- Write the answer. right
Check. 90 is exactly 90 degrees. ✓
Watch out. An angle of exactly 180 degrees is a straight line; more than 180 is reflex.
Method. Compare the size with 90 and 180 degrees.
- Compare with 90 and 180. 305 degrees is compared with the rules for each type.305 is between 180 and 360 degrees
- Name the angle. An angle that is between 180 and 360 degrees is reflex.reflex
- Write the answer. reflex
Check. 305 is between 180 and 360 degrees. ✓
Watch out. An angle of exactly 180 degrees is a straight line; more than 180 is reflex.
Method. A cube has six square faces.
- Count the faces. Each face is one square, and a cube has 6 square faces.6
- Write the answer. 6
Check. 6 faces. ✓
Method. Test each choice against the question.
- Read what the question asks. Decide what the answer must do or show.
- Test the choice. 60 degrees is exactly 60, so it is the closest.60 degrees fits
- Reject the other choices. 45 and 75 are 15 degrees away from 60, and 60 is 0 away.45 degrees and 75 degrees do not fit
- Write the answer. 60 degrees
Check. 60 degrees is the one that fits. ✓
Method. Test each option.
- Check each option. Test each one against the rule or the calculation.
- Tick the true ones. The radius is half of the diameter, and the diameter passes through the centre.The radius is half the diameter, The diameter goes through the centre
- Leave the others unticked. These do not match.The diameter is half the radius, The circumference is the distance across the middle are not ticked
- Write the answer. The radius is half the diameter, The diameter goes through the centre
Check. Each ticked option is true. ✓
Watch out. The distance around a circle is the circumference, not the diameter.
Method. Compare the size of the two angles.
- Right angle. A right angle is 90 degrees.90
- Obtuse angle. An obtuse angle is more than 90 degrees.more than 90
- Write the answer. obtuse
Check. obtuse is more than 90 degrees. ✓
Method. Check each angle against the rule for a reflex angle.
- Check 170. 170 is less than 180, so it is not reflex.not reflex
- Check 90. 90 is a right angle, so it is not reflex.not reflex
- Check 350. 350 is between 180 and 360, so it is reflex.350 is reflex
- Write the answer. 350
Check. 180 < 350 < 360. ✓
Method. Diameter = 2 x radius.
- Double the radius. 2 x 9 = 18.18
- Write the answer. 18
Check. 18 / 2 = 9. ✓
Method. Draw a circle with a line from the centre to the edge.
- Radius. The radius goes from the centre to the edge.centre to edge
- Diameter. Two radii joined together make a line across the circle, which is the diameter.two radii = diameter
- Write the answer. Because the diameter goes across the circle through the centre, and the radius is from the centre to the edge, so two radii make a diameter.
Check. 2 x radius = diameter. ✓