Geometry and measures worksheet — GCSE Foundation

1.A sector of a circle has radius 7 cm and angle 90°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

2.A furniture catalogue drawing uses a scale of 1 cm to 1.5 m. A sofa in the drawing is measured as 7 cm long. What is the real length of the sofa, in metres?

3.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.

4.Two similar signs have lengths in the ratio 9 : 4. The larger sign has a side of length 14.4 cm. Work out the length of the corresponding side of the smaller sign.

5.A right-angled triangle has a hypotenuse of 10 cm and one of its other angles is 45°. Work out the length of one of the two shorter sides. Give your answer to 1 decimal place.

6.A raised garden bed is a prism whose cross-section is a triangle with a base of 1.2 m and a perpendicular height of 0.8 m. The bed is 3 m long. Work out the volume of soil needed to fill it, in m³.

7.A running track has a straight section and a semicircular bend. The bend is a semicircle with radius 32 m. Work out the length of the curved part of the bend, to 1 decimal place. (Use π = 3.14.)

8.A shop stacks tins in a display block. The front elevation of the block is 4 tins wide and 3 tins high. The side elevation shows the block is 2 tins deep. Every position in the block is filled. How many tins are used in total?

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

10.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.

11.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.

12.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.

13.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.

14.A sector of a circle has angle 120° and an arc length of 31.4 cm. Using π = 3.14, work out the radius of the circle.

15.A solid cone has a base radius of 6 cm and a vertical height of 10 cm. Work out the volume of the cone. Use π = 3.14 and give your answer correct to 1 decimal place.