Geometry and measures worksheet — GCSE Foundation

1.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.

2.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.

3.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

4.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.

5.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.

6.A trapezium has an area of 45 cm², a perpendicular height of 5 cm, and one parallel side of length 10 cm. Work out the length of the other parallel side.

7.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

8.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

9.A solid metal sphere has a radius of 5 cm. It is melted down and recast into a solid cylinder with the same radius, 5 cm. Work out the height of the cylinder, so that its volume equals the volume of the sphere. Use π = 3.14 and give your answer correct to 1 decimal place.

10.A textbook contains the instruction 'Draw AB' and, on the next line, the statement 'AB = 5 cm'. Which statement about the notation AB is correct?

11.A ship sails 12 km on a bearing of 070° from a harbour to a buoy. It then sails a further 9 km, still on a bearing of 070°, from the buoy to a lighthouse. How far is the lighthouse from the harbour, in kilometres?

12.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

13.A footpath is 3750 m long. Work out this distance in kilometres.

14.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.

15.A shop sells rice in packs of 250 g. Aisha buys 4 packs. Work out the total mass of rice she buys, in kilograms.