Geometry and measures worksheet — GCSE Foundation

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

2.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.

3.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.

4.A television cable runs in a straight line from the edge of a flat roof 20 m above the ground to a bracket on a wall 5 m above the ground. The horizontal distance between the roof edge and the bracket is 15 m. Work out the length of the cable. Give your answer to 1 decimal place.

5.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.

6.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

7.A sector of a circle has an angle of 90° and an arc length of 15.7 cm. Using π = 3.14, work out the radius of the circle.

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

9.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.

10.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

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 solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.

13.A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. Work out its area.

14.A circular decoration has a radius of 10 cm. A ribbon costs £0.50 per centimetre and is fixed along the curved edge (the arc) of a sector-shaped section with an angle of 90°. Using π = 3.14, work out the cost of the ribbon for this section.

15.A sector of a circle has radius 6 cm and an arc length of 15.7 cm. Using π = 3.14, work out the angle of the sector.