OCR GCSE Maths
Topic questions Geometry and measures Circumference, area of circles & sectors
45 questions · 214 marks · about 3 hours
The shaded shape below is made from a right-angled triangle, ABC, and a semicircle. The length of AB is 20 cm and the diameter of the semicircle, BC, is of length 12 cm.
Calculate the perimeter of the shaded shape. You must show your working.
Also involves Forming and solving equations
The diagram shows a sector of a circle AOB and a circle with radius r cm.
The sector has radius 12 cm and angle AOB = 120°. The ratio of the area of the sector AOB to the area of the circle is 3: 4.
Calculate the value of r. You must show your working.
The diagram shows a sphere with radius r cm.
The sphere has a circumference of 50 cm.
Work out the surface area of the sphere.
[The surface area, A, of a sphere with radius r is A = 4πr2.]
The diagram shows a shape formed from a rectangle measuring 8 cm by 17 cm with a semicircle removed from one side.
Calculate the perimeter of the shape.
Also involves Arc length and sector area
The diagram shows a shape formed by a semicircle joined to a sector of a circle, BAC, along a common length AB.
The area of the sector BAC is 16π cm2.
Work out the total area of the shape. Give your answer in terms of π. You must show your working.
Also involves Rearranging formulae
The circumference of a circle is 17 cm.
Calculate the diameter of the circle. Give your answer correct to 1 decimal place.
A cylinder has a radius of 8.4 cm. The ratio of the radius of the cylinder to the height of the cylinder is 2: 5.
Find the volume of the cylinder.
The diagram shows a rectangle, OPQR, and a circle, centre O, which passes through Q. OR = 6 cm and RQ = 8 cm.
Find the circumference of the circle. Give your answer in terms of π.
AOB is a sector of a circle, centre O and radius 8 cm. Angle AOB = x °. The arc, AB, has length 2 cm. π
Find the area of the sector. Give your answer in terms of π.
A circle has radius 8 cm.
Work out the area of the circle.
Also involves Arc length and sector area
The diagram shows a circle, centre O and radius 52 cm.
AB is a chord of the circle. The line through T is a tangent to the circle.
The chord is parallel to the tangent. The perpendicular distance between the chord and the tangent is 72 cm.
Calculate the area of the shaded segment. You must show your working.
The shape below is part of a circle, centre O and radius 12 cm. Angle OAB = 30°.
Work out the perimeter of the shape.
The diagram shows a shaded sector inside a parallelogram. The sector has an angle of 30°. The parallelogram, ABCD, has length BC = 20 cm and AB = 12 cm. The perpendicular distance between BC and AD is 6 cm.
Show that the area of the sector is 37.7 cm2, correct to 3 significant figures.
Work out the percentage of the parallelogram that is not shaded.
Also involves Rounding
XOY is a sector of a circle, centre O.
Show that the area of the sector is 15.3 cm2, correct to 3 significant figures.
The diagram shows a Penny Farthing bicycle.
The diameter of the large wheel is 130 cm.
The diameter of the small wheel is 46 cm.
On a short journey, the large wheel makes exactly 69 rotations. The small wheel also makes an exact number of rotations.
Work out the number of rotations made by the small wheel.
In the diagram,
• ABC is a right-angled triangle
• ACD is the sector of a circle with centre A.
Show that the area of the sector ACD is 
m2.
Work out the total area of the shape ABCD.
Also involves Angle facts
This shape is formed from a rectangle and two sectors of circles.
Points A, B and C lie on a straight line. Angle CB D = 3 5 °. DE = 5 t and EF = 2 t.
Explain why BC = 2 t. Give a reason for each step of your explanation.
Show that the perimeter of the shape is 
t + 14t.
The diagram shows a circle inside a square of side 12 cm.
Work out the percentage of the square that is shaded. You must show your working.
The diagram shows a circle inside a square of side 12 cm.
Work out the percentage of the square that is shaded. You must show your working.
Also involves Forming and solving equations
Frankie draws a circle and works out its area, in cm2, and circumference, in cm. The answer for the area is two times the answer for the circumference.
Work out the diameter of the circle. You must show your working.
The diagram shows Kai’s garden. The garden is a rectangle, 16 m by 10 m.
It has a lawn and a flowerbed. The flowerbed is a circle of diameter 6 m.
Work out the area of Kai’s lawn.
Points A, B and C lie on the circumference of a circle, centre O.
Angle ACB = 90°, AC = 6.4 m and BC = 3.7 m.
Work out the circumference of the circle. You must show your working.
Also involves Simplifying and manipulating expressions
The diagram shows a shaded shape made by removing sector OAB from sector OCD. Both sectors have an angle of 60°. The radius, OA, of the smaller sector is r cm. The ratio of radius OA to radius OC is 2: 3.
Work out, in terms of π and r, the total length of arc AB and arc CD. Give your answer in its simplest form. You must show your working.
Also involves Rounding · Rearranging formulae
The circumference of a circle is 23 cm.
Show that the area of the circle is 42.1 cm2, correct to 3 significant figures.
A rectangle, 6 cm by 3 cm, and a semi-circle are joined to make this shape.
Work out the area of the shape.
Also involves Forming and solving equations
AOB is a sector of a circle, centre O and radius 10 cm.
The area of the sector is 40π cm2.
Work out the perimeter of the sector. Give your answer in the form a + b π, where a and b are integers. You must show your working.
Also involves Rounding · Using a calculator
The diagram shows Jane’s lawn. It is in the shape of a square of side 36 m and three semi-circles.
She is going to spread fertiliser on the lawn at a rate of 30 g per square metre. The fertiliser is only sold in 10 kg bags costing £15.80 each.
Calculate the cost of buying the bags of fertiliser for her lawn. You must show all your working.
Also involves Rearranging formulae
AOB is a sector of a circle, centre O.
The area of the sector is 8 cm2.
Work out the exact value of the radius, r cm.
Also involves Rounding
The diagram shows Jane’s lawn. It is in the shape of a square of side 36 m and three semi-circles.
She is going to spread fertiliser on the lawn at a rate of 30 g per square metre. The fertiliser is only sold in 10 kg bags costing £15.80 each.
Calculate the cost of buying the bags of fertiliser for her lawn. You must show all your working.
A circle has radius 5 cm.
Work out the circumference of the circle.
Work out the area of the circle.
Calculate the area of a circle with radius 14 cm.
AOB is a sector of a circle, centre O.
Show that the length of arc AB is 5.24 cm, correct to 3 significant figures.
The diagram shows a shape ABCDE. The shape is made from a rectangle, a right-angled triangle and a quarter of a circle.
F is the mid-point of BD. AE = 18 m and the perpendicular distance from C to AE is 41 m.
Work out the perimeter of the shape ABCDE.
OAB is a sector of a circle, centre O. OA = 6 cm and AX is perpendicular to OB.
The area of sector OAB is 6π cm2.
Calculate the circumference of a circle with diameter 10 cm.
Also involves Area and perimeter
A circle, with centre O and radius 6 cm, contains another circle, with centre O and radius x cm.
Write down an expression, in terms of π and x, for the shaded area in cm2.
Also involves Arc length and sector area
AOB is a sector of a circle, centre O and radius 6 cm. The length of arc AB is 5 π cm.
Find the area of the sector. Give your answer in terms of π.
Also involves Arc length and sector area
The shape below is formed from two semicircles and a straight line.
The radius of the large semicircle is 8 cm. The radius of the small semicircle is t cm.
Find an expression, in terms of t, for the exact perimeter of the shaded shape.
A circle has radius 6 cm.
Calculate its circumference. Give your answer in centimetres, correct to 1 decimal place.
Also involves Algebraic argument and proof
This shape consists of three semicircles.
The length of PQ is 4 x cm.
Show that the area, in cm2, of the whole shape is 3
x2.
A, B, C and D are points on the circumference of a circle, centre O.
Angle CAD = 28° and CD = 6.4 cm. BD is a diameter of the circle.
Calculate the area of the circle.
The design below is made from two sectors of circles, centre O.
Calculate the perimeter of the shaded part. Give your answer correct to 3 significant figures.
Also involves Area and perimeter
The following formula is for the area, A, of the curved surface area of a cone. A = π rl, where r is the radius and l is the slant height of the cone.
Calculate the total surface area of a cone with radius 5 cm and slant height 12 cm.
Also involves Pythagoras' theorem
The diagram shows a semi-circle inside a rectangle of length 120 m. The semi-circle touches the rectangle at A, B and C.
Calculate the perimeter of the shaded region. Give your answer correct to 3 significant figures.
Also involves Rounding
A sculpture is formed from a cylinder resting on top of a cuboid. The cylinder has radius 45 cm and height 80 cm. The cuboid measures 90 cm by 90 cm by 150 cm.
The sculpture is made of granite. The granite has a density of 2.7 g/cm3.
Calculate the total mass of the sculpture in tonnes.
Also involves Parts of a circle
The diagram shows a semi-circle inside a rectangle of length 120 m. The semi-circle touches the rectangle at A, B and C.
Calculate the perimeter of the shaded region. Give your answer correct to 3 significant figures.
Memes
Laugh now. Cry in the exam hall later. Then come back and do a past paper.
Mum 💖
did you do your maths homework sweetie?? 🥰
yes I solved for x
proud of you!!!
📱 Screen time this week · TikTok6h 7m
Maths starter pack