plumiCircles, surface area and volume: OCR GCSE Maths questions
Every OCR 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 35 questions on Circles, surface area and volume, as a list
- June 2025, Paper 4, Q3 (4 marks): The diagram shows a shape formed from a rectangle measuring 8 cm by 17 cm with a semicircle removed from one side. 4 cm 3 cm Not to scale 8 cm 17 cm Calculate t
- June 2025, Paper 5, Q19 (5 marks): The diagram shows a shape formed by a semicircle joined to a sector of a circle, BAC, along a common length AB. C Not to scale 40° A B The area of the sector BA
- June 2025, Paper 6, Q10 (5 marks): The diagram shows a sphere with radius 3 cm and a cube with side length x cm. x cm 3 cm x cm x cm The surface area of the sphere is equal to the surface area of
- November 2024, Paper 5, Q15 (8 marks): (a) The diagram shows a rectangle, OPQR, and a circle, centre O, which passes through Q. OR = 6 cm and RQ = 8 cm. Not to scale 8 cm R Q 6 cm O P Find the circum
- November 2024, Paper 6, Q10 (6 marks): A bowl in the shape of a hemisphere with radius 15 cm is used to collect raindrops. 15 cm - 4 Assume each raindrop has the volume of a sphere of radius 3 10 cm.
- June 2024, Paper 4, Q14 (6 marks): The diagram shows a circle, centre O and radius 52 cm. Not to scale A B 52 cm O 72 cm T AB is a chord of the circle. The line through T is a tangent to the circ
- June 2024, Paper 5, Q18 (4 marks): A sphere has radius x cm. A cone has radius R cm and height 2R cm. The volume of the sphere is equal to the volume of the cone. Write R in terms of x. 4 3 [The
- June 2024, Paper 6, Q5 (9 marks): The diagram shows a regular pentagon made using ten congruent right-angled triangles. The length of one side of the pentagon is 12 cm. Not to scale 12 cm 2, cor
- November 2023, Paper 6, Q11 (4 marks): The diagram shows a cone and a cube. The cone has radius 8 cm and height 10 cm. 10 cm 8 cm The volume of the cone is equal to the volume of the cube. Work out t
- November 2023, Paper 6, Q20 (7 marks): This shape is formed from a rectangle and two sectors of circles. C B 35° D Not to scale 5t A F E 2t Points A, B and C lie on a straight line. Angle CB D 3 ° 5
- June 2023, Paper 4, Q8 (6 marks): The diagram shows a circle inside a square of side 12 cm. 12 cm Work out the percentage of the square that is shaded. You must show your working. %
- June 2023, Paper 6, Q14 (7 marks): The diagram shows a square-based pyramid ABCDE. O is the centre of the base. E 14.5 cm 14.5 cm D C O 20 cm A 20 cm B The pyramid has base length 20 cm and each
- November 2022, Paper 4, Q12 (6 marks): The diagram shows a sphere and a cone. 15 cm Not to scale 4 cm 30 cm d cm The sphere has radius 4 cm. The cone has radius 15 cm and height 30 cm. The sphere is
- November 2022, Paper 6, Q7 (6 marks): A child has four identical wooden cubes of side length 6 cm. 6 cm (a) They arrange the cubes in a 2 by 2 by 1 arrangement to form a cuboid. 2. Show that the sur
- June 2022, Paper 4, Q7 (5 marks): The diagram shows a square-based pyramid and a sphere. r cm 15.7 cm 15.7 cm 12.3 cm 12.3 cm The pyramid has base length 12.3 cm and perpendicular height 15.7 cm
- June 2022, Paper 4, Q9 (5 marks): Points A, B and C lie on the circumference of a circle, centre O. Not to scale A O 6.4 m B 3.7 m C Angle ACB = 90°, AC = 6.4 m and BC = 3.7 m. Work out the circ
- June 2022, Paper 6, Q2 (4 marks): The circumference of a circle is 23 cm. Show that the area of the circle is 42.1 cm2, correct to 3 significant figures.
- June 2022, Paper 6, Q10 (6 marks): The diagram shows a triangular prism and a cube. The ends of the prism are right-angled triangles with base 16 cm and height 12 cm. The prism is 18 cm long. 12
- November 2021, Paper 6, Q12 (6 marks): A solid metal sphere has mass 235 g. The density of the metal is 7.78 g/cm3. Show that the surface area of this sphere is 46.9 cm2, correct to 3 significant fig
- November 2021, Paper 6, Q17 (5 marks): The diagram shows a pyramid ABCDE. E Not to scale 6.8 cm D C O 5.6 cm A B 5.6 cm The pyramid has a square horizontal base ABCD with side 5.6 cm. The vertex E is
- November 2020, Paper 4, Q6 (4 marks): A cuboid measures 6 cm by 8 cm by 15 cm. A cube has the same volume as the cuboid. Find the surface area of the cube, giving your answer correct to 3 significan
- November 2020, Paper 4, Q10 (6 marks): The diagram shows Jane’s lawn. It is in the shape of a square of side 36 m and three semi-circles. Not to scale She is going to spread fertiliser on the lawn at
- November 2020, Paper 6, Q14 (5 marks): The base of a cone is fixed to the top of a cylinder to make a decoration. 5r 6r r The radius of the base of the cone and of the cylinder is r cm. The cone’s he
- November 2019, Paper 6, Q8 (4 marks): An octahedron is formed from two identical square based pyramids. The square bases are stuck together as shown. h cm 3. The volume of the octahedron is 60 cm Th
- June 2019, Paper 4, Q7 (6 marks): The diagram shows a shape ABCDE. The shape is made from a rectangle, a right-angled triangle and a quarter of a circle. C Not to scale B D F 41 m A E 18 m F is
- June 2019, Paper 6, Q14 (5 marks): The length of the longest diagonal of a cube is 25 cm. Calculate the total surface area of the cube. cm2
- June 2019, Paper 6, Q18 (4 marks): A cone has radius r cm and height h cm. h cm r cm The height is three times the radius. 3. The volume of the cone is 2100 cm Calculate the radius of the cone. 1
- November 2018, Paper 4, Q6 (5 marks): The diagram shows a cylinder and a sphere. 12 cm r cm 30 cm The cylinder has radius 12 cm and height 30 cm. The cylinder and the sphere have the same volume. Wo
- November 2018, Paper 6, Q13 (3 marks): The shape below is formed from two semicircles and a straight line. Not to scale The radius of the large semicircle is 8 cm. The radius of the small semicircle
- June 2018, Paper 5, Q14 (5 marks): The diagram shows a cylinder and a cone. 2 cm h cm 9 cm r cm The cylinder has radius 2 cm and height 9 cm. The cone has radius r cm and height h cm. The ratio r
- June 2018, Paper 6, Q13 (7 marks): (a) Calculate the volume of a sphere with radius 6 cm. 6 cm 4 3 [The volume V of a sphere with radius r is . ] V r r = 3 cm3 (a) (b) An ornament is made from a
- November 2017, Paper 6, Q8 (5 marks): The design below is made from two sectors of circles, centre O. 6 cm 45° O 3.5 cm Calculate the perimeter of the shaded part. Give your answer correct to 3 sign
- November 2017, Paper 6, Q15 (3 marks): The following formula is for the area, A, of the curved surface area of a cone. A = rrl, where r is the radius and l is the slant height of the cone. Calculate
- June 2017, Paper 4, Q6 (5 marks): The diagram shows a semi-circle inside a rectangle of length 120 m. The semi-circle touches the rectangle at A, B and C. Not to scale B A C 120 m Calculate the
- June 2017, Paper 6, Q8 (5 marks): The object below is made from a square-based pyramid joined to a cuboid. 13 cm 8 cm 4 cm The base of the cuboid and the base of the pyramid are both squares of
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