IGCSE Maths Mensuration topical questions

Convert between units.

1. (a)Write 2.8 m in centimetres.[1]
2. (b)Write 0.6 m² in cm².[1]
3. (c)A bottle holds 3500 cm³ of juice. Write this in litres.[2]

A rectangular garden measures 9 m by 6 m.

1. (a)Find the perimeter of the garden.[1]
2. (b)Find the area of the garden.[1]
3. (c)Fencing costs $13 per metre. Find the total cost of fencing the perimeter.[2]

A rectangular swimming pool is 25 m long, 10 m wide and 2 m deep.

1. (a)Find the volume of water needed to fill the pool, in m³.[2]
2. (b)Write this capacity in litres.[2]
3. (c)The pool fills at 500 litres per minute. Find the filling time in hours and minutes.[2]

A prism has a trapezium cross-section with parallel sides 10 cm and 16 cm and perpendicular height 6 cm. The prism is 12 cm long.

1. (a)Find the area of the trapezium cross-section.[2]
2. (b)Find the volume of the prism.[3]

A circle has a diameter of 14 cm.

1. (a)Find the circumference, giving your answer to 3 significant figures.[2]
2. (b)Find the area, giving your answer to 3 significant figures.[3]

A sector of a circle has radius 10 cm and angle 72°.

1. (a)Find the arc length, to 3 significant figures.[2]
2. (b)Find the sector area, to 3 significant figures.[3]

A closed cylindrical tin has radius 5 cm and height 12 cm.

1. (a)Find the volume of the tin, to 3 significant figures.[2]
2. (b)Find the total surface area of the tin, to 3 significant figures.[3]

An L-shaped floor is made from a 6 m by 4 m rectangle with a 3 m by 2 m rectangle attached to its right-hand end, flush with the bottom edge.

1. (a)Find the total floor area.[3]
2. (b)Find the perimeter of the whole floor.[3]

A sector of a circle has area 12π cm² and radius 6 cm.

1. (a)Find the angle of the sector.[3]
2. (b)Find the arc length of the sector.[2]
3. (c)Write down the perimeter of the sector.[1]

A water trough is a prism whose trapezium cross-section has parallel sides 40 cm and 20 cm and perpendicular depth 30 cm. The trough is 120 cm long.

1. (a)Find the area of the cross-section.[2]
2. (b)Find the volume of the trough, in cm³.[2]
3. (c)Write down the capacity of the trough, in litres.[2]
4. (d)The trough is filled to three quarters of its capacity. How many litres of water does it hold?[1]

A right cone has radius 6 cm and perpendicular height 8 cm. (Extended)

1. (a)Show that the slant height is 10 cm.[1]
2. (b)Find the volume of the cone, to 3 significant figures.[2]
3. (c)Find the total surface area of the cone, to 3 significant figures.[3]

A solid hemisphere has radius 5 cm. (Extended)

1. (a)Find the volume of the hemisphere, to 3 significant figures.[3]
2. (b)Find the total surface area of the hemisphere (curved surface plus the flat circular face), to 3 significant figures.[3]

A cone has volume 96π cm³ and base radius 6 cm. (Extended)

1. (a)Find the perpendicular height of the cone.[3]
2. (b)Find the slant height of the cone.[2]
3. (c)Find the curved surface area of the cone, giving your answer in terms of π.[2]

A solid metal ball of radius 6 cm is melted and recast into identical smaller balls of radius 2 cm. (Extended)

1. (a)Show that the volume of the large ball is 27 times the volume of a small ball.[3]
2. (b)Write down the number of small balls made.[1]
3. (c)Show that the total surface area of all the small balls is three times the surface area of the large ball.[3]