GCSE Maths Mensuration questions by topic

One rectangle, two measures.

1. (a)A rectangle measures 7 cm by 12 cm. Find its perimeter.[2]
2. (b)Find its area.[2]

Triangle and parallelogram.

1. (a)A triangle has base 14 cm and perpendicular height 6 cm. Find its area.[2]
2. (b)A parallelogram has base 9 cm and perpendicular height 5 cm. Find its area.[2]

Trapezium and L-shape.

1. (a)A trapezium has parallel sides 6 cm and 10 cm with a perpendicular height of 5 cm. Find its area.[2]
2. (b)An L-shape is made from a 9 cm × 7 cm rectangle with a 4 cm × 2 cm corner removed. Find its area.[2]

Unit conversions.

1. (a)Write 3.2 m in cm.[1]
2. (b)Write 0.6 litres in cm³.[1]
3. (c)Write 520 mm in cm, and 2.4 kg in g.[2]

A corner is cut from a rectangle.

1. (a)A rectangle measures 8 m by 5 m. A 3 m by 2 m rectangle is removed from one corner. Work out the remaining area.[2]
2. (b)Work out the perimeter of the remaining shape, and comment on your answer.[2]

A roundabout is measured.

1. (a)A roundabout is a circle of diameter 14 m. Using π = 22⁄7, work out its circumference.[2]
2. (b)Using π = 22⁄7, work out its area.[2]

One radius, two circle answers.

1. (a)A circle has radius 4.5 cm. Find its circumference, to 1 decimal place.[2]
2. (b)Find its area, to 1 decimal place.[3]

A large sector.

1. (a)A sector of a circle has radius 12 cm and angle 210° at the centre. Find the arc length, to 1 decimal place.[3]
2. (b)Find the sector’s area, to 1 decimal place.[2]

Volumes of a cuboid and a cylinder.

1. (a)A cuboid measures 6 cm by 9 cm by 5 cm. Find its volume.[2]
2. (b)A cylinder has radius 10 cm and height 4 cm. Find its volume, to 1 decimal place.[3]

Surface areas.

1. (a)A closed cuboid measures 4 cm by 3 cm by 5 cm. Find its total surface area.[3]
2. (b)A cylinder has radius 2 cm and height 9 cm. Find its total surface area (two caps plus the curved wall), to 1 decimal place.[2]

A triangular trough is filled.

1. (a)A trough is a prism whose cross-section is a right-angled triangle with legs 40 cm and 30 cm, and it runs 1 m long. Work out the cross-section area.[2]
2. (b)Work out the volume of the trough in cm³, then convert it to litres.[3]

A cone with a 3-4-5 inside. (Higher)

1. (a)A cone has radius 6 cm and vertical height 8 cm. Show that its slant height is 10 cm.[2]
2. (b)Find the volume of the cone, to 1 decimal place.[2]
3. (c)Find the total surface area (curved surface plus base), to 1 decimal place.[2]

A sphere and its half. (Higher)

1. (a)A sphere has radius 9 cm. Find its volume, to 1 decimal place.[3]
2. (b)Find its surface area, to 1 decimal place.[2]
3. (c)Write down the volume of a hemisphere of the same radius, to 1 decimal place.[1]

A silo: cylinder plus hemisphere. (Higher)

1. (a)A solid silo is a cylinder of radius 5 m and height 10 m with a hemisphere on top. Find the cylinder’s volume, to 1 decimal place.[2]
2. (b)Find the hemisphere’s volume, to 1 decimal place.[2]
3. (c)Find the total volume of the silo, to 1 decimal place.[2]

A trapezium trough. (Higher)

1. (a)A trough’s cross-section is a trapezium with parallel sides 8 cm and 12 cm and perpendicular height 9 cm. Find the cross-section area.[2]
2. (b)The trough is 25 cm long. Find its volume.[2]
3. (c)Explain why volume = cross-section area × length applies to this trough.[2]

Slant, surface and capacity of a cone. (Higher)

1. (a)A cone has base radius 6 cm and vertical height 8 cm. Work out its slant height.[2]
2. (b)Work out the curved surface area, to 1 decimal place.[2]
3. (c)Work out the volume, to 1 decimal place.[2]

A silo capacity is totalled. (Higher)

1. (a)A silo is a cylinder of radius 4 m and height 10 m, topped by a hemisphere of radius 4 m. Work out the volume of the hemisphere, to 1 decimal place.[2]
2. (b)Work out the volume of the cylinder, to 1 decimal place.[2]
3. (c)Work out the total capacity to 3 significant figures.[2]

Two similar cylinders are compared. (Higher)

1. (a)A small cylinder has radius 2 cm, and a similar large one has radius 5 cm. Work out the length scale factor.[1]
2. (b)The small cylinder is 5 cm tall. Work out the height of the large one.[1]
3. (c)The small cylinder’s volume is 20π cm³. Work out the volume of the large cylinder, to 1 decimal place.[4]