plumiCircles, surface area and volume: AQA GCSE Maths questions
Every AQA GCSE Maths exam question on G17 Circles, surface area and volume, 2017–2025, with its mark scheme and examiner’s report.
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All 41 questions on Circles, surface area and volume, as a list
- June 2025, Paper 2H, Q8 (4 marks): Here is a circle, centre O. Not drawn accurately 8 (a) The circle has a circumference of 20 cm Assume that angle x is 90° Work out the shaded area. Give your an
- June 2025, Paper 3H, Q21 (4 marks): Five identical spheres just fit inside a cylinder. Each sphere has radius r. Volume of a sphere = r3 4 3 π What fraction of the space inside the cylinder is fil
- November 2024, Paper 1H, Q7 (4 marks): A large circle and a small circle are shown. The radius of the large circle is 12cm radius of large circle : radius of small circle = 4 : 1 Not drawn accurately
- November 2024, Paper 3H, Q22 (4 marks): The metal used to make a sphere costs £4320 The metal costs £3.60 per gram. Each cubic centimetre of metal has a mass of 17.3 grams. Work out the radius, r, of
- June 2024, Paper 1H, Q7 (4 marks): Here is a cone. 7 (a) Curved surface area of a cone = πrl where r is the radius and l is the slant height Beth tries to work out the curved surface area in term
- June 2024, Paper 3H, Q21 (5 marks): A cylinder, C, and a sphere, S, each have radius r C has height h Volume of a sphere = πr3 where r is the radius 21 (a) volume of C = volume of S Work out the r
- November 2023, Paper 3H, Q14 (4 marks): A solid trophy consists of a stand and a player. Trophy The stand is made by removing a small pyramid from a large pyramid. Large pyramid Square base, edge 8 cm
- November 2023, Paper 3H, Q23 (4 marks): A chocolate box in the shape of a prism is being designed. All lengths are in centimetres. The cross section is a regular hexagon with side x The length is 5x A
- June 2023, Paper 1H, Q17 (3 marks): A solid hemisphere has radius x. A solid cylinder has radius 3x and height x. Work out the ratio total surface area of the hemisphere : total surface area of th
- June 2023, Paper 1H, Q26 (4 marks): A circle, centre O, has circumference 20πcm Q is a point on the circle. OPQR is a square. Not drawn accurately perimeter of the square : circumference of the ci
- June 2023, Paper 2H, Q11 (4 marks): A bowl is a hemisphere with radius 12 cm Volume of a sphere = 4 3 πr3 Water is poured into the bowl at a rate of 325 cm3 per second for 8 seconds. Does the wate
- June 2023, Paper 3H, Q6 (2 marks): Here is cuboid A. Cuboid B is made from two of cuboid A. volume of A : volume of B = 1 : 2 Matthew says, “surface area of A : surface area of B must be 1 : 2 be
- November 2022, Paper 2H, Q8 (3 marks): (a) Here is a cuboid. w, x and y are different whole numbers. The total length of all the edges of the cuboid is 80 cm The volume is greater than 200 cm3 Work o
- November 2022, Paper 3H, Q11 (4 marks): Part of a running track is the arc of a semicircle joined to a straight line. The semicircle has diameter 45 metres. The straight line has length 75 metres. Not
- November 2022, Paper 3H, Q23 (5 marks): Alec makes a bowl for dog food from a solid wooden cone. The sketches show how the bowl is made. The cone has radius 9 cm and perpendicular height 30 cm A small
- June 2022, Paper 1H, Q11 (4 marks): Here are two shapes, P and Q. Not drawn accurately How many times bigger is the area of P than the area of Q? You must show your working. Answer
- June 2022, Paper 2H, Q13 (7 marks): Outside a cafe there is a large plastic ice cream cornet. The cornet is a hemisphere on top of a cone. The cone and the hemisphere each have radius 24 cm The co
- June 2022, Paper 3H, Q16 (5 marks): Here is a scale drawing of a reservoir. Scale: 1 cm represents 500 m Virat wants to estimate the volume of water in the reservoir. He draws on the scale drawing
- November 2021, Paper 1H, Q27 (4 marks): The vertices of a regular hexagon lie on a circle with centre O and radius 5 cm Work out the shaded area. Give your answer in the form a b c − 12 π where a, b a
- November 2021, Paper 2H, Q9 (4 marks): A ball contains 5000 cm3 of air. More air is pumped into the ball at a rate of 160 cm3 per second. The ball is full of air when it becomes a sphere with radius
- November 2020, Paper 1H, Q8 (3 marks): The shorter side of a parallelogram has length 6.5 cm The length of the shorter side is 1 9 of the perimeter. Work out the length of the longer side. Not drawn
- November 2020, Paper 2H, Q9 (4 marks): Here is a cuboid. 9 (a) Assume that the total surface area of the cuboid is 200 cm2 Work out the volume of the cuboid. Answer cm3 9 (b) In fact, the total surfa
- November 2020, Paper 3H, Q29 (5 marks): A shape is made by joining triangle ABC to a semicircle with diameter AC. Not drawn accurately Work out the total area of the shape. Answer cm2
- November 2019, Paper 1H, Q9 (4 marks): Here are two solids. Cylinder radius 4 cm height 10 cm Hemisphere radius 6 cm volume of a hemisphere = 2 3 πr3 where r is the radius Which solid has the greater
- June 2019, Paper 1H, Q9 (4 marks): A shaded semicircle is inside a circle as shown. The radius of the circle is 10 cm The diameter of the semicircle is 8 cm How many times bigger is the unshaded
- June 2019, Paper 2H, Q21 (3 marks): A solid shape is made by joining two cones. Each cone has the same radius. One cone has slant height = 2 × radius The other cone has slant height = 3 × radius T
- November 2018, Paper 2H, Q5 (1 mark): A circle has circumference C and diameter d. C = kd What value does the constant k represent? Answer
- November 2018, Paper 2H, Q8 (4 marks): Two identical quarter circles are cut from a rectangle as shown. Work out the shaded area. Not drawn accurately Answer cm2
- November 2018, Paper 3H, Q9 (5 marks): A motor racing circuit consists of two parallel straight sections, each of length 0.75 km a semicircle of diameter 0.9 km three equal, smaller semicircles. The
- November 2018, Paper 3H, Q15 (5 marks): A company makes two types of lampshade using fabric on wire frames. Lampshade A Fabric is used to make the curved surface of a cylinder. The cylinder has radius
- November 2018, Paper 3H, Q24 (4 marks): A sphere has radius 2x cm A cone has radius 3x cm perpendicular height h cm The sphere and the cone have the same volume. Work out radius of cone : perpendicula
- June 2018, Paper 1H, Q11 (4 marks): A large rectangle is made by joining three identical small rectangles as shown. The perimeter of one small rectangle is 15 cm Work out the perimeter of the larg
- June 2018, Paper 1H, Q18 (5 marks): Here is a tunnel for a toy train. The diagram below shows the cross section of the tunnel. Not drawn accurately AD is a semicircular arc of radius 10 cm BC is a
- June 2018, Paper 2H, Q10 (3 marks): A container is a hemisphere of radius 30 cm Sand fills the container at a rate of 4000 cm3 per minute. Does it take less than a quarter of an hour to fill the c
- November 2017, Paper 1H, Q7 (2 marks): Here is a quarter circle of radius 6 cm Work out the area of the quarter circle. Give your answer in terms of π. Not drawn accurately Answer cm2
- November 2017, Paper 2H, Q22 (5 marks): The cross section of an earring is a semicircle, centre C, radius 25 mm The earring is black and white. The shaded area is black. Not drawn accurately Sector BC
- November 2017, Paper 3H, Q27 (6 marks): VABCD is a square-based pyramid. The horizontal base ABCD has side length 10 cm and centre M. Angle VMA is 90° Angle VAM is 68° Volume of pyramid = 3 1 × area o
- June 2017, Paper 1H, Q12 (3 marks): Here is a circle touching a square. The area of the square is 64 cm2 Work out the area of the circle. Give your answer in terms of π. Not drawn accurately Answe
- June 2017, Paper 1H, Q28 (4 marks): Volume of cone = 3 1 πr2h where r is the radius and h is the perpendicular height. A cone has a horizontal base of radius 5 cm height of 15 cm The cone contains
- Specimen, Paper 2H, Q17 (5 marks): The distance from the Earth to the Sun is 93 million miles. Assume it takes 365 days for the Earth to travel once around the Sun the Earth travels in a circle w
- Specimen, Paper 2H, Q23 (4 marks): A bowl is a hemisphere with radius 6 cm Water fills two-fifths of the volume of the bowl. The water is poured into a hollow cone. The depth of the water in the
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