Mathematics 0580 · IGCSE
Surface area and volume
100 practice questions on Surface area and volume, with worked solutions and instant marking.
The cuboid measures 12 m by 15 m by 20 m.
Feb/March 2017
Explain why these rectangles are similar in the mathematical sense.
Feb/March 2018
The diagram represents a solid prism measuring 15.2 cm in length. Its cross-section is a regular hexagon with side 7 cm.
Feb/March 2018
A cuboid is drawn with side lengths of 12 cm, 5 cm and 7.5 cm. This sketch is not drawn to scale.
Feb/March 2019
The diagram illustrates a net for a solid.
Feb/March 2019
Calculate the cuboid's total surface area.
Feb/March 2019
Calculate the cone's radius.
Feb/March 2019
A cuboid has a length of 3 cm, a width of 2 cm and a height of 1 cm.
Feb/March 2020
Calculate the number of litres of water she now uses each day.
Feb/March 2020
A cone made of solid metal has a radius of 1.65 cm and a slant height of 4.70 cm.
Feb/March 2020
The diagram depicts a prism. Its cross-section is an equilateral triangle. The diagram includes dimensions marked 4 cm and 3 cm and is labelled NOT TO SCALE.
Feb/March 2021
The diagram depicts one face of a cuboid on a $1\text{ cm}^2$ grid. The cuboid’s volume is $24\text{ cm}^3$.
Feb/March 2023
A cylinder partly filled with water is shown. A solid metal sphere is resting on the base of the cylinder, and half of the sphere is submerged in the water. The cylinder has radius 12 cm and the sphere has radius 3 cm.
Feb/March 2023
The diagram shows a cuboid net. The labelled measurements are 10 cm across the top rectangle, 4 cm for the vertical side of that rectangle, and 5 cm for the vertical side of the rectangle on the right. The diagram is marked NOT TO SCALE.
Feb/March 2024
The figure is the net of a cuboid, and the base is shaded. The cuboid has length 10 cm, width 4 cm and height 5 cm. The lengths on the diagram are marked as $a$ cm, $b$ cm, $c$ cm and $d$ cm. The shaded rectangle is labelled Base. The diagram is drawn NOT TO SCALE.
Feb/March 2024
The figure depicts a pyramid with square base $BCDE$. The diagonals $CE$ and $BD$ meet at $M$, and vertex $F$ is vertically above $M$. $BE = 12$ cm and $FM = 9$ cm.
Feb/March 2024
The diagram depicts a triangular prism. $ABC$ is an isosceles triangle with $AC = BC$. The perpendicular height of triangle $ABC$ measures 4 cm. $AB = 6$ cm and $BD = 6$ cm.
Feb/March 2025
The sketch depicts a cylinder with radius $r$ cm and height $16$ cm. A sphere with radius $3$ cm is also given. The cylinder and the sphere have equal volumes.
Feb/March 2025
A cuboid has dimensions 3 cm, 7 cm and 11 cm. Calculate its surface area.
Feb/March 2025
The cone’s sloping edge measures $12\text{ cm}$, and its base radius is $5\text{ cm}$.
Feb/March 2025
The volume of a cuboid is $288\,\text{cm}^3$.
May/June 2015
The diagram depicts the barn's front elevation. The barn has a width of 12 m and a height of 8 m. Each side of the barn is 5 m high.
May/June 2015
Calculate the cylinder's volume.
May/June 2015
The sketch presents the barn's front elevation. The barn is 12 m wide and 8 m tall. Each side of the barn has a height of 5 m.
May/June 2015
The diagram shows a solid pyramid on a square horizontal base $ABCD$ (not drawn to scale). The diagonals $AC$ and $BD$ meet at $M$. $P$ is directly above $M$. $AB = 20$ cm and $PM = 8$ cm.
May/June 2015
Find the value of $x$.
May/June 2015
A sector is used to make a cone and a plant pot.
May/June 2015
Calculate the volume for this cuboid.
May/June 2016
A trapezium is drawn and marked NOT TO SCALE. Its parallel sides measure 7 cm and 10 cm. The perpendicular distance between the parallel sides is 6 cm.
May/June 2016
A solid is formed from a metal cube from which a hemisphere has been removed. Each edge of the cube measures 7 cm. The hemisphere has diameter 5 cm. The diagram is NOT TO SCALE. For a sphere of radius $r$, the volume $V$ is given by $V=\frac{4}{3}\pi r^3$.
May/June 2016
A cuboid’s dimensions are length 4 cm, width 3 cm and height 1.5 cm.
May/June 2016
The sketch is of a cylindrical flower vase with radius $r$ and height $h$. Its volume $V$ is given by $V = \pi r^2 h$. Its surface area $A$ is given by $A = 2\pi r h + \pi r^2$. The sketch is not drawn to scale.
May/June 2016
Calculate the volume of a metal sphere with radius $15\,\text{cm}$ and verify that it rounds to $14\,140\,\text{cm}^3$, correct to 4 significant figures. [The volume, $V$, of a sphere with radius $r$ is $V=\frac{4}{3}\pi r^3$.]
May/June 2016
The diagram depicts a cuboid with vertices $A, B, C, D, E, F, G, H$.\nIts dimensions are $AD = 60$ cm, $CD = 35$ cm and $CG = 30$ cm. The diagram is not drawn to scale.
May/June 2016
The diagram illustrates a sector with centre $O$ and radius 12 cm. Angle $AOB = 145^\circ$.
May/June 2016
A cuboid measures 6 cm in length, 5 cm in width and 3 cm in height. On the 1 $\text{cm}^2$ grid, complete the net for the cuboid. The base has already been drawn.
May/June 2017
Each diagram displays the net of a solid.
May/June 2017
Find the area of a circle with radius $6$ cm.
May/June 2017
For a sphere whose radius is $r$, the volume $V$ is given by $V = \frac{4}{3}\pi r^{3}$.
May/June 2017
The diagram depicts a cylindrical coffee container used in a hotel. Its height is 50 cm and its radius is 18 cm.
May/June 2017
The diagram depicts a hollow cone whose radius measures 3 cm and whose slant height is 10 cm.
May/June 2017
Calculate the area of cross section ABCDE.
May/June 2017
A solid’s net is shown on a $1\text{ cm}^2$ grid, and the diagram displays that net.
May/June 2018
The diagram depicts a solid cuboid (NOT TO SCALE) whose base area is $7\text{ cm}^2$. Its volume is $21\text{ cm}^3$.
May/June 2018
A glass in the shape of a cylinder has radius 3.6 cm and height 11 cm, and it is filled with water.
May/June 2018
Find the surface area of this cuboid.
May/June 2018
The hemisphere is solid and has a volume of 230 cm$^3$.
May/June 2018
Calculate how much water passes through the pipe in 1 hour. Give your answer in litres.
May/June 2018
A cuboid has a volume of $180\text{ cm}^3$, and its base is a square with side length $6\text{ cm}$.
May/June 2019
A closed cuboid-shaped box measures 5 cm in length, 4 cm in width and 2 cm in height.
May/June 2019
The volume of a cuboid is $180\text{ cm}^3$. Its base is a square with side length 6 cm.
May/June 2019
A cylinder with a radius of 6 cm and a height of 17 cm is given. Show that the volume of this cylinder is $1923\,\text{cm}^3$, correct to 4 significant figures.
May/June 2019
The diagram displays the surface of a garden pond, which is made up of a rectangle and two semicircles. The rectangle is $3$m by $1.2$m. The drawing is marked NOT TO SCALE.
May/June 2019
The solid metal sphere has a volume of 24 430 cm$^3$.
May/June 2019
The diagrams depict a hemispherical bowl, a cylindrical tin and a cone.
May/June 2019
A cuboid has volume $24\text{ cm}^3$. Its base measures 3 cm by 2 cm. A 1 cm$^2$ grid is supplied.
May/June 2021
The cuboid shown has a square base, with volume $867\text{ cm}^3$ and height $12\text{ cm}$.
May/June 2021
Calculate the volume of a cylindrical vase whose radius is $14.2\text{ cm}$ and whose height is $18\text{ cm}$.
May/June 2021
The diagram depicts a box in the form of a cuboid. Its top is open. The cuboid measures length $5\text{ cm}$, width $2\text{ cm}$, and height $4\text{ cm}$. The diagram is labelled NOT TO SCALE.
May/June 2021
The diagrams depict a solid cone together with a solid hemisphere. The cone has radius 2.4 cm and slant height 6.3 cm. The hemisphere has radius $R$ cm. The cone's total surface area is the same as the hemisphere's total surface area. For a cone with radius $r$ and slant height $l$, the curved surface area, $A$, is $A = \pi r l$. For a sphere with radius $r$, the curved surface area, $A$, is $A = 4\pi r^2$. (b) The diagram shows a solid cone with radius 7.6 cm and height 16 cm. A cut is made parallel to the base of the cone and the top section is removed. The remaining solid has height 12 cm. For a cone with radius $r$ and height $h$, the volume, $V$, is $V = \frac{1}{3}\pi r^2 h$.
May/June 2021
The diagram depicts prism $ABCDEF$. The measurements given are $AB = 13$ cm, $AC = 20$ cm, $CF = 24$ cm, and angle $ABC = 90^{\circ}$.
May/June 2021
Determine the total surface area of a cuboid with length 8 cm, width 6 cm and height 3 cm.
May/June 2022
A cuboid-shaped box has a volume of $357\,\text{cm}^3$. Its length is $8.5\,\text{cm}$ and its width is $6\,\text{cm}$.
May/June 2022
The diagram depicts a solid metal object formed from a cone and a hemisphere, each with radius $6.2\text{ cm}$. The solid’s total surface area is $600\text{ cm}^2$. For a sphere of radius $r$, the curved surface area, $A$, is $A = 4\pi r^2$. For a cone of radius $r$ and slant height $l$, the curved surface area, $A$, is $A = \pi r l$.
May/June 2022
Work out the total surface area of a cuboid whose length is $8\text{ cm}$, width is $6\text{ cm}$ and height is $3\text{ cm}$.
May/June 2022
On the $1\text{ cm}^2$ grid, finish a net for this prism. One face is already shown.
May/June 2022
ABCDEFGH is a regular octagon with side length $6$ cm. The diagram displays only part of the octagon. $O$ denotes the centre of the octagon and $M$ is the midpoint of $AB$.
May/June 2022
A rectangular piece of paper $ABCD$ is formed into an open cylinder by making edge $AB$ meet edge $DC$. $AD = 28\,\text{cm}$ and $AB = 20\,\text{cm}$.
May/June 2022
Calculate the volume of a sphere with a diameter of 4.8 cm. [For a sphere of radius $r$, the volume $V$ is given by $V = \frac{4}{3}\pi r^3$.]
May/June 2023
A right-angled triangular prism is shown in a diagram. The triangular end has sides marked 3 cm, 4 cm and 5 cm, and the prism length is 6 cm. The diagram is NOT TO SCALE. On the 1 cm$^2$ grid, one face has already been drawn for you.
May/June 2023
A cuboid is illustrated, and the diagram is not drawn to scale. The dimensions given are length 8 cm, width 3 cm and height 5 cm.
May/June 2023
The diagram depicts a triangular prism. Each triangular face has side lengths of 4 cm, and the prism’s length is 2 cm. The diagram is not drawn to scale.
May/June 2023
Calculate the volume for a sphere with diameter $4.8\text{ cm}$. [$\text{The volume, } V, \text{ of a sphere with radius } r \text{ is } V = \frac{4}{3}\pi r^3.$]
May/June 2023
Calculate the radius of the cylinder.
May/June 2023
The diagram depicts a cuboid, drawn not to scale, with the labelled dimensions length 8 cm, width 3 cm and height 5 cm.
May/June 2023
The net of a solid is drawn on a $1\text{ cm}^2$ grid. The net includes the labelled points A, B, C, D, E, F, G, H, I, J, K, L, M and N.
May/June 2023
Calculate the volume occupied by the cone.
May/June 2023
The cuboid is drawn with side lengths of $15\text{ cm}$, $6\text{ cm}$ and a height of $h\text{ cm}$. NOT TO SCALE.
May/June 2024
The area of a circle is given as $36\pi\text{ cm}^2$.
May/June 2024
On the 1 cm$^2$ grid, finish a net for this cuboid. One face has already been drawn.
May/June 2024
Calculate how many complete times the jug may be filled with water from the tank.
May/June 2024
Calculate the height of the cuboid.
May/June 2024
A cuboid has a base that is 10 cm by 7 cm. Its volume is $280\text{ cm}^3$.
May/June 2024
Calculate the area of the inside of the open box.
May/June 2024
Write the perimeter of the shaded shape $ABDC$ in the form $(a\pi + b)\,\text{cm}$. Determine the value of $a$ and the value of $b$.
May/June 2024
Calculate the solid's total surface area.
May/June 2024
Calculate the volume for a cube with a side length of 3 cm.
May/June 2025
A cuboid is displayed, not to scale, with the dimensions marked as length 6 cm, height 4 cm and width 3 cm.
May/June 2025
The cuboid measures 5 cm in length, 2 cm in width and 3 cm in height.
May/June 2025
The diagram displays two faces from a cuboid net on a 1 $\text{cm}^2$ grid.
May/June 2025
The net of a square-based pyramid is shown in the diagram. NOT TO SCALE. Each triangular face has a perpendicular height of 4 cm. The square base has side length 5 cm.
May/June 2025
The solid is formed by attaching a hemisphere to a cylinder. Both the hemisphere and the cylinder have radius 6 cm. The cylinder has height 5 cm.
May/June 2025
A cylinder has a volume of $863.5\text{ cm}^3$, and its height measures $12.3\text{ cm}$.
May/June 2025
A gold bar, shaped as a cuboid, measures $2\text{ cm}$ by $4\text{ cm}$ by $6.5\text{ cm}$. Gold has a density of $19.32\text{ g/cm}^3$. The formula provided is: Density = mass / volume.
May/June 2025
The diagram depicts a solid cylinder with a height of 10 cm. It is marked NOT TO SCALE. The cylinder has a volume of 478 $\text{cm}^3$.
May/June 2025
The diagram presents the net of a solid shape.
May/June 2025
A cone made entirely from wood has a base radius of 4 cm and a height of 12 cm. The wood’s density is 0.74 g/cm$^3$. [Density = Mass \div Volume]
May/June 2025
The diagram depicts a solid cuboid whose edges measure $4.5\text{ cm}$, $8\text{ cm}$ and $13.2\text{ cm}$. The drawings are NOT TO SCALE.
May/June 2025
The diagram depicts a frustum formed by cutting away a smaller cone from a larger cone. The height of the smaller cone is $7.5\text{ cm}$. The height of the frustum is $4.5\text{ cm}$. The radius of the larger cone is $4.2\text{ cm}$. The diagram is NOT TO SCALE.
May/June 2025
A cuboid is drawn with edges measuring 5 cm, 12.5 cm and 9 cm. The illustration is labelled NOT TO SCALE.
Oct/Nov 2015