Areas and volumes of prisms - Edexcel GCSE Maths (Calculator) Exam Questions

Practise 36 exam-style questions on Areas and volumes of prisms for Edexcel GCSE Maths (Calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.

36 questions
1–5 marks each
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20 questions, marked as you go

Sample questions with model answers

Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.

Question 1

2 marks

The diagram shows a trapezium ABCD.
AB is parallel to DC.

Work out the area of the trapezium.

Geometry diagram, marked "Diagram NOT accurately drawn". Trapezium ABCD. A dashed line is drawn from D going downwards. The angle at an unlabelled point between the lines to D and B is marked as a right angle (90°). Side AB is labelled 11.9 cm. Side DC is labelled 7.3 cm. The line going downwards from D is labelled 5.6 cm. AB and DC are each marked with an arrowhead (parallel lines).

Model answer

Area \(= \frac{1}{2}(a + b)h\)
\(= \frac{1}{2}(7.3 + 11.9) \times 5.6\)
\(= \frac{1}{2} \times 19.2 \times 5.6 = 53.76\) cm²

Explanation

For a trapezium, add the two parallel sides, halve the total (this gives the average width) and multiply by the perpendicular distance between the parallel sides. A common slip is to multiply 7.3 × 11.9 or to forget the half.

Mark scheme

1 mark
M1 for \(\frac{1}{2}(7.3 + 11.9) \times 5.6\) oe
e.g. splitting into a rectangle and triangles correctly
1 mark
A1 for 53.76 cm²
cao; correct answer with no working scores full marks

Question 2

3 marks

A rectangle measures 12.8 cm by 5.7 cm.
A triangle has a base of 9.5 cm.
The triangle has the same area as the rectangle.

Work out the perpendicular height of the triangle.

Model answer

Area of rectangle \(= 12.8 \times 5.7 = 72.96\) cm²
\(\frac{1}{2} \times 9.5 \times h = 72.96\)
\(4.75h = 72.96\)
\(h = 72.96 \div 4.75 = 15.36\) cm

Explanation

Set the triangle's area formula equal to the rectangle's area and solve for the height. Remember the half: dividing 72.96 by 9.5 without doubling gives 7.68 cm, half the correct height.

Mark scheme

1 mark
P1 for \(12.8 \times 5.7\) (= 72.96 cm²)
1 mark
P1 for \(\frac{1}{2} \times 9.5 \times h = 72.96\) or \(h = 72.96 \times 2 \div 9.5\)
ft their area
1 mark
A1 for 15.36 cm
cao; accept 15.4; correct answer with no working scores full marks

Question 3

3 marks

A jug is in the shape of a cylinder.
The jug holds 1.5 litres of water when it is full.
The height of the jug is 18 cm.

Work out the radius of the jug.
Give your answer correct to 3 significant figures.

Model answer

1.5 litres = 1500 cm³
\(\pi r^2 \times 18 = 1500\)
\(r^2 = \dfrac{1500}{18\pi} = 26.52...\)
\(r = \sqrt{26.52...} = 5.150...\)
r = 5.15 cm (3 s.f.)

Explanation

Change litres into cm³, substitute into \(V = \pi r^2 h\) and rearrange for \(r^2\). Remember the final square root - 26.5 cm would be the value of \(r^2\), not the radius.

Mark scheme

1 mark
M1 for \(\pi r^2 \times 18 = 1500\)
1.5 litres = 1500 cm³
1 mark
M1 for \(r^2 = \dfrac{1500}{18\pi}\) (= 26.5...) or \(r = \sqrt{\dfrac{1500}{18\pi}}\)
1 mark
A1 for 5.15 cm
awrt 5.15 (5.150...); correct answer with no working scores full marks

Question 4

5 marks

The diagram shows a swimming pool in the shape of a prism.
The pool is 12 m long and 6 m wide.
The depth of the pool increases steadily from 0.9 m at the shallow end to 2.1 m at the deep end.

The empty pool is filled with water at a rate of 250 litres per minute.

How long does it take to fill the pool completely?
Give your answer in hours and minutes.

A prism drawn in 3D with hidden edges shown as dashed lines. Its front face (the cross-section) is a 4-sided shape with corners at (0, 0), (12, 1.2), (12, 2.1), (0, 2.1) (in order). The length of the prism is labelled 6 m (along the edge going back from the lowest right-hand corner of the front face). On the front face, the edge from corner 2 to corner 3 is labelled 0.9 m, the edge from corner 3 to corner 4 is labelled 12 m and the edge from corner 4 to corner 1 is labelled 2.1 m. The diagram is labelled "Diagram NOT accurately drawn".

Model answer

The cross-section is a trapezium with parallel sides 0.9 m and 2.1 m, 12 m apart.
Area \(= \frac{1}{2}(0.9 + 2.1) \times 12 = 18\) m²
Volume \(= 18 \times 6 = 108\) m³ = 108 000 litres
Time \(= 108\,000 \div 250 = 432\) minutes
\(432 = 7 \times 60 + 12\)
7 hours 12 minutes

Explanation

The pool is a prism: its side view is a trapezium (the two depths are the parallel sides and the length is the distance between them), and the width is the length of the prism. Convert m³ into litres (× 1000) to match the filling rate, then change the minutes into hours and minutes. 432 minutes is not 4.32 hours.

Mark scheme

1 mark
P1 for the area of the trapezium cross-section \(\frac{1}{2}(0.9 + 2.1) \times 12\) (= 18 m²)
1 mark
P1 for their area \(\times 6\) (= 108 m³)
1 mark
P1 for 108 m³ = 108 000 litres
1 m³ = 1000 litres
1 mark
P1 for their 108 000 \(\div 250\) (= 432 minutes)
1 mark
A1 for 7 hours 12 minutes
cao; correct answer with no working scores full marks

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