IGCSEMathsCambridge (CIE)CoreExam QuestionsLengths, Areas & VolumesVolume & Surface Area

Volume & Surface Area (Cambridge (CIE) IGCSE Maths: Core)

Exam Questions

1 hour23 questions
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1
Sme Calculator3 marks
qp11-0580-12-paper-1-nov-2020-cie-igcse-maths

The diagram shows cuboid A and cuboid B.
Cuboid A has the same volume as cuboidspace B.

Calculate the height,h, of cuboid B.

h space equals ...................................... cm

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2
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The length of the edge of a cube is 8 cm.
Calculate the surface area of this cube.

............................................. cm2 

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3
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qp16-0580-12-paper-1-oct-nov-2019-cie-igcse-maths

The diagram shows a cuboid measuring 15cm by 12 cm by 4 cm.

Calculate the surface area of the cuboid.

............................................. cm2 

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4
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A cuboid measures 5cm by 7cm by 9.5 cm.

qp16-0580-13-paper-1-oct-nov-2019-cie-igcse-maths

Work out the surface area of this cuboid.

............................................. cm2

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5
Sme Calculator3 marks

These two cuboids have the same volume.

qp7c-0580-33-paper-3-oct-nov-2019-cie-igcse-maths

Find the value of h.

h space= ...................................................

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6
Sme Calculator1 mark

The diagram shows a solid cuboid made of identical cubes.

q14a-058012-mayjune2019-cie-igcse-maths-core

Work out the number of cubes in the cuboid.

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7
Sme Calculator2 marks

A closed box in the shape of a cuboid has length 5cm, width 4 cm and height 2cm.

Calculate the volume of the box.

................................. cm3

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8
Sme Calculator3 marks
q21-058012-march2019-cie-igcse-maths-core

Calculate the total surface area of the cuboid.

................................cm2

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9
Sme Calculator6 marks

The diagram shows a cuboid.

q1c-058032-march2018-cie-igcse-maths-core

i) Work out the surface area of this cuboid.

.......................... cm2 [3]

ii) Work out the volume of this cuboid.

.............................. cm3 [2]

iii) Write down the dimensions of a different cuboid that has the same volume as this cuboid.

..................... cm by ..................... cm by ..................... cm [1]

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10a
Sme Calculator3 marks

A cuboid measures 5cm by 4 cm by 2cm.

Calculate the volume of this cuboid.

Give the units of your answer.

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10b
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On the 1 cm2 grid, draw an accurate net of this cuboid.

One face has been drawn for you.

A grid with a central rectangle outlined in bold black lines, occupying six by four grid squares. The rectangle is centred within the larger grid.

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1a
Sme Calculator3 marks
qp6-0580-31-paper-3-nov-2020-cie-igcse-maths

The diagram shows a right-angled triangular prism.

On the 1 cm2 grid, complete the net of the prism.

One face has been drawn for you.

qp6a-0580-31-paper-3-nov-2020-cie-igcse-maths

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1b
Sme Calculator3 marks

Work out the surface area of the prism.

.......................................... cm2 

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1c
Sme Calculator2 marks

Work out the volume of the prism.

.......................................... cm3 

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2
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A plant pot is a cylinder with radius 15 cm and height 24 cm.

Calculate the volume of the pot.

.......................................... cm3 

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3
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A cone has radius 4.5 cm and height 10.4 cm.

Calculate, in terms of pi, the volume of the cone.

[The volume, V, of a cone with radius r and height h is V equals 1 third pi r squared h]

.......................................... cm3 

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4a
Sme Calculator1 mark

The diagram shows the net of a triangular prism on a 1cm2 grid.

qp3-0580-31-paper-3-may-2020-cie-igcse-maths

Write down the mathematical name for the type of triangle shown on the grid.

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4b
Sme Calculator5 marks

i) Measure the perpendicular height of the triangle.

............................................ cm [1]

ii) Calculate the area of the triangle.

.......................................... cm2 [2]

iii) Calculate the volume of the triangular prism.

.......................................... cm3 [2]

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5a
Sme Calculator3 marks

A cube has a surface area of 384cm2.

Find the length of one of its sides.

............................................ cm

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5b
Sme Calculator3 marks
qp6c-0580-32-paper-3-may-2020-cie-igcse-maths

The diagram shows a right-angled triangular prism.

Work out the volume of the prism.

.......................................... cm3

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6
Sme Calculator2 marks

The radius of a sphere is 5.2cm.

Work out the surface area of this sphere.

[The surface area, A, of a sphere with radius r is space A space= 4pi r2.]

......................................... cm2 

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7
Sme Calculator2 marks

The volume of a cuboid is 180 cm3.

The base is a square of side length 6cm.

Calculate the height of this cuboid.

....................................... cm 

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8
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A cylinder has a radius of 6 cm and a height of 17 cm.

Show that the volume of this cylinder is 1923 cm3, correct to 4 significant figures.

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1
Sme Calculator4 marks

A solid cylinder has radius 3cm and height 4.5cm.

Calculate the total surface area of the cylinder.

.......................................... cm2 

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2
Sme Calculator3 marks

A cube has a volume of 1000cm3 .
Calculate the surface area of the cube.

......................................... cm2 

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3
Sme Calculator2 marks
qp4d-0580-32-paper-3-oct-nov-2019-cie-igcse-maths

Another glass is in the shape of a cylinder.

The cylinder has height 15cm and diameter 7cm.

Calculate the volume of the glass.

............................................. cm3 

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4
Sme Calculator6 marks

A cake is made by putting a small cylinder of cake on top of a large cylinder of cake.

The radius of the large cylinder is 15cm. The radius of the small cylinder is 8cm. The height of each cylinder is 10cm.

q7b-058031-octnov2018-cie-igcse-maths-core

i) Calculate the total volume of the cake.

................................cm3 [3]

ii) Nora wraps a ribbon around the large cylinder. The ribbon is 4 cm longer than needed to go all the way around this cylinder.

Calculate the length of this ribbon.

.............................. cm [3]

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5
Sme Calculator7 marks

The diagram shows a hollow metal pipe in the shape of a cylinder.

q5e-058032-octnov2018-cie-igcse-maths-core

i) This diagram shows the cross-section of the pipe.

q5ei-058032-octnov2018-cie-igcse-maths-core

Work out the shaded area.

............................cm2 [3]

ii)The cylinder is 18cm long. Work out the volume of the metal.

.........................cm3 [1]

iii) Work out the curved surface area of the outside of the pipe.

.............................cm2 [3]

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