Geometry and measures worksheet — GCSE Foundation

1.In triangle ABC and triangle DEF, AB = DE, angle ABC = angle DEF and BC = EF. Write down the congruence condition that proves the two triangles are congruent.

2.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.

3.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

4.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

5.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

6.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.

7.In a right-angled triangle one of the other two angles is 45°, and the side opposite that 45° angle is 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.

8.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?

9.The angle between north and a footpath is 35°, measured clockwise from north. What is the three-figure bearing of the footpath?

10.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.

11.An ice cream is made from a cone of radius 3 cm and height 10 cm, topped with a hemisphere of the same radius sitting exactly on top of the cone. Work out the total volume of the ice cream. Use π = 3.14. Give your answer to the nearest whole number. Volume of a cone = 1/3 × πr²h. Volume of a sphere = 4/3 × πr³.

12.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

13.A square has sides of length 7 cm. Work out its area.

14.A plan of a school hall uses a scale of 1 : 250. A wall is drawn 3.4 cm long on the plan. Sam wants to know the wall's real length in metres. What is it?

15.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.