2022 May/June · Paper 41 · Q5 (a(ii), b(i), b(ii))11 marksCircles, arcs & sectors · Surface area & volume
2022 May/June · Paper 42 · Q11 (a(i), a(ii), b)9 marksSurface area & volume
2022 May/June · Paper 43 · Q4 (b(ii)(a), b(ii)(b), c)7 marksCircles, arcs & sectors · Surface area & volume
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Practice questions
Original questions written by HomiLabs in the style of the exam, with answers and mark schemes. They are not
Cambridge past paper questions and have not been reviewed by Cambridge. Try each one before opening the answer.
Q1Surface area & volume · Core · Paper 3 style · calculator · 3 marks
(a)A water tank on a roof in Multan is a cuboid measuring 1.2 m by 0.8 m by 0.6 m.Calculate the volume of the tank in m³.[2]
(b)1 m³ = 1000 litres. How many litres of water does the tank hold when it is full?[1]
Show answer
(a) 0.576 m³
M1 1.2 × 0.8 × 0.6A1 0.576
(b) 576 litres
B1 follow through 0.576 × 1000
Q2Surface area & volume · Core · Paper 1 style · no calculator · 3 marks
(a)A box is a cuboid measuring 5 cm by 4 cm by 3 cm.Work out the volume of the box.[1]
(b)Work out the total surface area of the box.[2]
Show answer
(a) 60 cm³
B1
(b) 94 cm²
M1 2(5 × 4 + 5 × 3 + 4 × 3)A1 94
Q3Surface area & volume · Core · Paper 3 style · calculator · 4 marks
(a)A tin of food is a cylinder with radius 4 cm and height 10 cm.Calculate the volume of the tin. Give your answer correct to 3 significant figures.[2]
(b)A paper label covers the curved surface of the tin exactly.Calculate the area of the label.[2]
Show answer
(a) 503 cm³
M1 π × 4² × 10A1 503 (502.65…)
(b) 251 cm²
M1 2 × π × 4 × 10A1 251 (251.32…)
Q4Surface area & volume · Core · Paper 3 style · calculator · 5 marks
A wooden doorstop is a prism. Its cross-section is a right-angled triangle with the two shorter sides 6 cm and 8 cm. The length of the prism is 15 cm.
(a)Calculate the volume of the doorstop.[2]
(b)The longest side of the triangle is 10 cm.Calculate the total surface area of the doorstop.[3]
Show answer
(a) 360 cm³
M1 ½ × 6 × 8 × 15A1 360
(b) 408 cm²
M1 two triangles: 2 × 24 = 48M1 three rectangles: (6 + 8 + 10) × 15 = 360A1 408
Q5Surface area & volume · Standard · Paper 4 style · calculator · 6 marks
(a)A solid cone has base radius 6 cm and perpendicular height 8 cm.Show that the slant height of the cone is 10 cm.[1]
(b)Calculate the total surface area of the cone. Give your answer correct to 3 significant figures.[Curved surface area of a cone = πrl][3]
(c)Calculate the volume of the cone.[Volume of a cone = ⅓πr²h][2]
Q6Surface area & volume · Standard · Paper 4 style · calculator · 5 marks
(a)A solid metal sphere has a volume of 500 cm³.Calculate the radius of the sphere. Give your answer correct to 3 significant figures.[Volume of a sphere = 4/3 πr³][3]
(b)Calculate the surface area of the sphere. Give your answer correct to 3 significant figures.[Surface area of a sphere = 4πr²][2]
M1 4 × π × (4.9237…)²A1 305 (304.6…); 304 from using r = 4.92 accepted
Q7Surface area & volume · Standard · Paper 2 style · no calculator · 5 marks
(a)A solid hemisphere has radius 6 cm.Find the volume of the hemisphere. Give your answer in terms of π.[Volume of a sphere = 4/3 πr³][2]
(b)Find the total surface area of the solid hemisphere, including its flat face. Give your answer in terms of π.[Surface area of a sphere = 4πr²][3]
Show answer
(a) 144π cm³
M1 ½ × 4/3 × π × 6³A1 144π
(b) 108π cm²
M1 ½ × 4π × 6² = 72πM1 + π × 6² = 36πA1 108π
Q8Surface area & volume · Standard · Paper 3 style · calculator · 3 marks
(a)A cylindrical container has a volume of 1000 cm³ and a radius of 5 cm.Calculate the height of the container. Give your answer correct to 3 significant figures.[2]
(b)A second cylinder has the same volume but its radius is 10 cm.Without further calculation of π, explain why its height is one quarter of the height in part (a).[1]
Show answer
(a) 12.7 cm
M1 π × 5² × h = 1000A1 12.7 (12.73…)
(b) Doubling the radius multiplies the base area by 4, so the height must be divided by 4 for the same volume
B1
Q9Surface area & volume · Standard · Paper 4 style · calculator · 6 marks
(a)A solid pyramid has a square base of side 10 cm. Its vertex is vertically above the centre of the base and its perpendicular height is 12 cm.Calculate the volume of the pyramid.[Volume of a pyramid = ⅓ × base area × height][2]
(b)Show that the height of each triangular face, measured from the midpoint of a base edge to the vertex, is 13 cm.[2]
(c)Calculate the total surface area of the pyramid.[2]
Show answer
(a) 400 cm³
M1 ⅓ × 100 × 12A1 400
(b) √(12² + 5²) = 13
M1 right-angled triangle with sides 12 and 5A1 √169 = 13
(c) 360 cm²
M1 100 + 4 × ½ × 10 × 13A1 360
Q10Surface area & volume · Standard · Paper 3 style · calculator · 4 marks
(a)A swimming pool is a cuboid 25 m long, 10 m wide and 1.8 m deep.Calculate the volume of the pool in litres. [1 m³ = 1000 litres][2]
(b)The empty pool is filled with water at a rate of 300 litres per minute.How many hours does it take to fill the pool completely?[2]
Show answer
(a) 450 000 litres
M1 25 × 10 × 1.8 = 450 m³A1 450 000
(b) 25 hours
M1 450 000 ÷ 300 = 1500 minutesA1 25 hours
Q11Surface area & volume · Challenge · Paper 4 style · calculator · 6 marks
(a)A cylindrical jug has radius 5 cm and height 18 cm. It is full of water.All the water is poured into an empty cuboid tank with a horizontal base measuring 20 cm by 15 cm.Calculate the depth of water in the tank. Give your answer correct to 3 significant figures.[3]
(b)More water is then poured into the tank at a rate of 0.25 litres per second until the depth of water is 12 cm.Calculate the time taken. Give your answer correct to the nearest second. [1 litre = 1000 cm³][3]
Q12Surface area & volume · Challenge · Paper 4 style · calculator · 7 marks
(a)A solid is made from a cylinder of radius 3 cm and height 10 cm with a cone of radius 3 cm and perpendicular height 4 cm fixed to its top face.Calculate the total volume of the solid. Give your answer correct to 3 significant figures.[Volume of a cone = ⅓πr²h][3]
(b)Calculate the total surface area of the solid. Give your answer correct to 3 significant figures.[Curved surface area of a cone = πrl][4]
Q13Surface area & volume · Challenge · Paper 3 style · calculator · 4 marks
(a)A solid metal sphere of radius 6 cm is melted down. All the metal is used to make small solid cones, each with base radius 2 cm and perpendicular height 3 cm.Calculate the number of cones made.[Volume of a sphere = 4/3 πr³, Volume of a cone = ⅓πr²h][4]
Q14Surface area & volume · Challenge · Paper 2 style · no calculator · 4 marks
(a)A solid cone has base radius 6 cm and perpendicular height 12 cm. A small cone of perpendicular height 4 cm is cut off the top by a cut parallel to the base, leaving a frustum.Find the radius of the small cone.[1]
(b)Find the volume of the frustum. Give your answer in terms of π.[Volume of a cone = ⅓πr²h][3]
Q15Circles, arcs & sectors · Core · Paper 1 style · no calculator · 2 marks
(a)A circle has radius 7 cm.Find the circumference of the circle. Give your answer in terms of π.[1]
(b)Find the area of the circle. Give your answer in terms of π.[1]
Show answer
(a) 14π cm
B1
(b) 49π cm²
B1
Q16Circles, arcs & sectors · Core · Paper 3 style · calculator · 4 marks
(a)A circular flower bed in a park in Islamabad has diameter 12.6 m.Calculate the circumference of the flower bed. Give your answer correct to 3 significant figures.[2]
(b)Calculate the area of the flower bed. Give your answer correct to 3 significant figures.[2]
Show answer
(a) 39.6 m
M1 π × 12.6A1 39.6 (39.58…)
(b) 125 m²
M1 π × 6.3²A1 125 (124.68…)
Q17Circles, arcs & sectors · Standard · Paper 4 style · calculator · 5 marks
(a)A sector of a circle has radius 9 cm and angle 140°.Calculate the length of the arc. Give your answer correct to 3 significant figures.[2]
(b)Calculate the perimeter of the sector.[1]
(c)Calculate the area of the sector. Give your answer correct to 3 significant figures.[2]
Show answer
(a) 22.0 cm
M1 140/360 × 2 × π × 9A1 22.0 (21.99…)
(b) 40.0 cm
B1 21.99… + 18 = 39.99… = 40.0
(c) 99.0 cm²
M1 140/360 × π × 9²A1 99.0 (98.96…)
Q18Circles, arcs & sectors · Standard · Paper 2 style · no calculator · 4 marks
(a)A sector of a circle has radius 12 cm and angle 150°.Find the area of the sector. Give your answer in terms of π.[2]
(b)Find the perimeter of the sector. Give your answer in terms of π.[2]
Show answer
(a) 60π cm²
M1 150/360 × π × 144A1 60π
(b) (24 + 10π) cm
M1 arc = 150/360 × 2π × 12 = 10πA1 24 + 10π
Q19Circles, arcs & sectors · Standard · Paper 3 style · calculator · 4 marks
(a)The wheel of a bicycle has diameter 64 cm.Calculate the distance travelled, in cm, when the wheel makes one complete turn. Give your answer correct to 1 decimal place.[2]
(b)Calculate the number of complete turns the wheel makes when the bicycle travels 1 km.[2]
Show answer
(a) 201.1 cm
M1 π × 64A1 201.1
(b) 497
M1 100 000 ÷ (64π) = 497.35…A1 497
Q20Circles, arcs & sectors · Challenge · Paper 4 style · calculator · 5 marks
(a)A sector of a circle has radius 8 cm and area 50 cm².Calculate the angle of the sector. Give your answer correct to 1 decimal place.[3]
(b)Calculate the arc length of this sector. Give your answer correct to 3 significant figures.[2]
M1 89.52…/360 × 2 × π × 8 (or 2 × area ÷ r = 100 ÷ 8)A1 12.5
Q21Circles, arcs & sectors · Challenge · Paper 4 style · calculator · 4 marks
(a)O is the centre of a circle of radius 10 cm. A and B are points on the circle and angle AOB = 70°.Calculate the area of the minor segment cut off by the chord AB. Give your answer correct to 3 significant figures.[Area of triangle = ½ab sin C][4]
Q22Circles, arcs & sectors · Challenge · Paper 2 style · no calculator · 5 marks
(a)A sector of a circle with radius 15 cm and angle 216° is cut from card. The two straight edges are joined to make a hollow cone with no gaps or overlaps.Show that the base radius of the cone is 9 cm.[2]
(b)Find the perpendicular height of the cone.[1]
(c)Find the volume of the cone. Give your answer in terms of π.[Volume of a cone = ⅓πr²h][2]
Q23Area & perimeter · Core · Paper 1 style · no calculator · 2 marks
(a)A rectangular carpet measures 12 m by 7.5 m.Work out the area of the carpet.[1]
(b)Work out the perimeter of the carpet.[1]
Show answer
(a) 90 m²
B1
(b) 39 m
B1
Q24Area & perimeter · Core · Paper 1 style · no calculator · 2 marks
(a)A trapezium has parallel sides of length 9 cm and 15 cm. The perpendicular distance between the parallel sides is 6 cm.Work out the area of the trapezium.[Area of a trapezium = ½(a + b)h][2]
Show answer
(a) 72 cm²
M1 ½ × (9 + 15) × 6A1 72
Q25Area & perimeter · Standard · Paper 3 style · calculator · 4 marks
(a)A room floor is L-shaped. It is a rectangle 8 m by 6 m with a rectangle 3 m by 2.5 m removed from one corner.Calculate the area of the floor.[2]
(b)Write down the perimeter of the floor.[1]
(c)Floor tiles cost Rs 1850 per square metre.Calculate the cost of tiling the whole floor.[1]
Show answer
(a) 40.5 m²
M1 8 × 6 − 3 × 2.5A1 40.5
(b) 28 m
B1 same as the full rectangle: 2(8 + 6)
(c) Rs 74 925
B1 40.5 × 1850
Q26Area & perimeter · Standard · Paper 3 style · calculator · 4 marks
(a)A parallelogram has area 91 cm² and base 14 cm.Calculate the perpendicular height of the parallelogram.[2]
(b)A triangle has the same area as the parallelogram and the same base length.Calculate the perpendicular height of the triangle.[2]
Show answer
(a) 6.5 cm
M1 91 ÷ 14A1 6.5
(b) 13 cm
M1 ½ × 14 × h = 91A1 13
Q27Area & perimeter · Challenge · Paper 4 style · calculator · 5 marks
(a)A rectangle has length (x + 5) cm and width (x − 2) cm. Its area is 60 cm².Show that x² + 3x − 70 = 0.[2]
(b)Solve the equation and find the perimeter of the rectangle.[3]
M1 (x + 10)(x − 7) = 0A1 x = 7 (x = −10 rejected as the width would be negative)A1 2(12 + 5) = 34
Q28Area & perimeter · Challenge · Paper 2 style · no calculator · 4 marks
(a)A logo is made from a square of side 10 cm with a semicircle drawn outwards on one side of the square, using that side as the diameter.Find the perimeter of the logo. Give your answer in terms of π.[2]
(b)Find the area of the logo. Give your answer in terms of π.[2]
Show answer
(a) (30 + 5π) cm
M1 semicircle arc = ½ × π × 10 = 5πA1 30 + 5π
(b) (100 + 12.5π) cm²
M1 ½ × π × 5² = 12.5πA1 100 + 12.5π
Q29Units of measure · Core · Paper 1 style · no calculator · 3 marks
(a)Change 3.5 m² into cm².[1]
(b)Change 2.4 litres into cm³.[1]
(c)Change 4500 g into kg.[1]
Show answer
(a) 35 000 cm²
B1 3.5 × 10 000
(b) 2400 cm³
B1
(c) 4.5 kg
B1
Q30Units of measure · Standard · Paper 3 style · calculator · 5 marks
(a)Change 0.75 m³ into litres.[1]
(b)A train travels at 72 km/h. Change this speed into metres per second.[2]
(c)The density of aluminium is 2.7 g/cm³. Change this density into kg/m³.[2]
Show answer
(a) 750 litres
B1
(b) 20 m/s
M1 72 × 1000 ÷ 3600A1 20
(c) 2700 kg/m³
M1 2.7 × 1 000 000 ÷ 1000A1 2700
Similar questions
Questions that test the same subtopic in different years, grouped so you can work on one skill at a time.
References only: find each question in its paper (official link where available, otherwise through your school).
Surface area & volumeBanker96 questions · 9/9 sessions
