Volume & Surface Area (Cambridge International IGCSE Maths): Exam Questions

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

Calculate the height,$h$, of cuboid $B$.

$h=$ ...................................... cm

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

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

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

Calculate the surface area of the cuboid.

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

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

Work out the surface area of this cuboid.

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

These two cuboids have the same volume.

Find the value of $h$.

$h$= ...................................................

The diagram shows a solid cuboid made of identical cubes.

Work out the number of cubes in the cuboid.

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

Calculate the total surface area of the cuboid.

................................cm²

The diagram shows a cuboid.

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]

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

Calculate the volume of this cuboid.

Give the units of your answer.

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.

Work out the surface area of the prism.

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

Extract:

The diagram shows a right-angled triangular prism.

Work out the volume of the prism.

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

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

Calculate the volume of the pot.

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

A cone has radius 4.5 cm and height 10.4 cm.

Calculate, in terms of $π$, the volume of the cone.

[The volume, $V$, of a cone with radius $r$ and height $h$ is $V=\frac{1}{3}πr^{2}h$]

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

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

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

Extract:

The diagram shows the net of a triangular prism on a 1cm^2 grid.

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]

A cube has a surface area of 384cm².

Find the length of one of its sides.

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

The diagram shows a right-angled triangular prism.

Work out the volume of the prism.

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

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 $A$= 4$πr$².]

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

The volume of a cuboid is 180 cm³.

The base is a square of side length 6cm.

Calculate the height of this cuboid.

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

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.

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

Calculate the total surface area of the cylinder.

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

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

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

Another glass is in the shape of a cylinder.

The cylinder has height 15cm and diameter 7cm.

Calculate the volume of the glass.

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

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.

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]

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

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

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]