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Either paper 3 marks
Think about a hexagonal prism.
(a)How many faces does it have?
(b)How many edges does it have?
(c)How many vertices does it have?
Show answer
(a) \(8\)
(b) \(18\)
(c) \(12\)A hexagonal prism is made of two hexagonal ends and six rectangles.
That gives \(8\) faces.
An edge is where two faces meet.
A hexagonal prism has \(18\) edges.
A vertex is a corner, where three or more edges meet.
A hexagonal prism has \(12\) vertices.
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Either paper 3 marks
A traffic cone is a cone.
(A face is flat. A curved surface is not flat, so it is described separately. An edge is where two surfaces meet.)
(a)How many flat faces does it have?
(b)How many curved surfaces does it have?
(c)How many edges does it have?
Show answer
(a) \(1\)
(b) \(1\)
(c) \(1\)A cone has \(1\) flat face(s) — circle.
A cone has \(1\) curved surface, because the single circle is joined to the point by one curved surface.
An edge is where two surfaces meet, so a cone has \(1\).
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Either paper 1 mark
Which of these is a correct statement about this solid?
Tick one.
- It has 8 edges. - It has 8 faces. - It has 8 planes. - It has 8 vertices.
Show answer
It has 8 vertices.Count each kind of element on the solid, including the dashed edges you cannot see from this side.
The cuboid has 6 faces, 12 edges and 8 vertices.
Every statement uses the number \(8\), so only the element that really has \(8\) of them makes a correct statement. "Planes" is not a name for part of a solid.
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Either paper 3 marks
Here are five solids. Dashed lines show edges you cannot see from this side.
(a)How many faces does the cuboid have?
(b)How many edges does the pentagonal prism have?
(c)How many faces does the triangular prism have?
Show answer
(a) \(6\)
(b) \(15\)
(c) \(5\)A cuboid has 6 rectangular faces: top, bottom and four sides.
A pentagonal prism has 5 edges round each end and 5 joining the ends: 5 + 5 + 5 = 15 edges.
A triangular prism has 2 triangular ends and 3 rectangular sides: 2 + 3 = 5 faces.
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Either paper 2 marks
A solid has \(5\) faces, \(8\) edges and \(5\) vertices, and four triangles meet at a point above a square.
Write down the name of the solid.
Show answer
square-based pyramidCounting up: \(5\) faces, \(8\) edges and \(5\) vertices, and four triangles meet at a point above a square.
That is a square-based pyramid.
- M1uses the clue (four triangles meet at a point above a square) to identify the type of solid (prism or pyramid and its base shape)
- A1name the solid: square-based pyramid
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Either paper 4 marks
The diagram shows a cuboid. The dashed lines are the edges you cannot see from this side.
(a)State the number of faces.
(b)State the number of edges.
(c)State the number of vertices.
(d)Find the volume of the cuboid.
Show answer
(a) \(6\)
(b) \(12\)
(c) \(8\)
(d) \(84\ \text{cm³}\)The faces come in opposite pairs: front and back, left and right, top and bottom. That is \(6\).
Four edges run each way, and there are three directions: \(4 \times 3 = 12\).
Three of them are the dashed ones hidden behind the solid.
A corner at each end of the four vertical edges: \(8\).
\(7 \times 2 \times 6 = 84\) cm³
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Either paper 5 marks
The diagram shows a triangular prism.
(a)State the number of faces.
(b)State the number of edges.
(c)State the number of vertices.
(d)Find the volume of the prism.
Show answer
(a) \(5\)
(b) \(9\)
(c) \(6\)
(d) \(312\ \text{cm³}\)Two triangular ends and three rectangles between them: \(5\).
Three round each triangle, and three joining them: \(3 + 3 + 3 = 9\).
Three corners on each triangle: \(6\).
The cross-section is a triangle with base \(8\) cm and height \(6\) cm:
\(\frac{1}{2} \times 8 \times 6 = 24\) cm²
A prism's volume is its cross-section times its length:
\(24 \times 13 = 312\) cm³
- (d) M1cross-section \(\frac{1}{2} \times 8 \times 6 = 24\) cm²
- (d) A1volume \(24 \times 13 = 312\) cm³
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Either paper 2 marks
A pyramid has \(7\) faces and \(12\) edges.
Euler's formula for a solid with flat faces is \(F + V - E = 2\).
Use it to work out how many vertices the pyramid has.
Show answer
\(7\)Substitute what you know into \(F + V - E = 2\):
\(7 + V - 12 = 2\)
\(V - 12 + 7 = 2\), so \(V = 2 + 12 - 7\)
\(V = 7\)
The pyramid has \(7\) vertices.
- M1substitute into Euler: \(7 + V - 12 = 2\)
- A1\(V = 7\)
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Either paper 3 marks
Think about a hexagonal prism.
(a)How many faces does it have?
(b)How many edges does it have?
(c)How many vertices does it have?
Show answer
(a) \(8\)
(b) \(18\)
(c) \(12\)A hexagonal prism is made of two hexagonal ends and six rectangles.
That gives \(8\) faces.
An edge is where two faces meet.
A hexagonal prism has \(18\) edges.
A vertex is a corner, where three or more edges meet.
A hexagonal prism has \(12\) vertices.
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Either paper 3 marks
A tin of soup is a cylinder.
(A face is flat. A curved surface is not flat, so it is described separately. An edge is where two surfaces meet.)
(a)How many flat faces does it have?
(b)How many curved surfaces does it have?
(c)How many edges does it have?
Show answer
(a) \(2\)
(b) \(1\)
(c) \(2\)A cylinder has \(2\) flat face(s) — circles.
A cylinder has \(1\) curved surface, because the two circles are joined by one curved surface that wraps all the way round.
An edge is where two surfaces meet, so a cylinder has \(2\).