Geometry and measures worksheet — GCSE Foundation

1.A jug holds 750 ml of water. Work out what fraction of a litre this is.

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

3.A square-based pyramid is cut by a flat plane parallel to its base, partway up between the base and the apex. What shape is the cross-section?

4.A tank holds 3.2 m³ of water. Work out this volume in litres.

5.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.

6.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

7.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.

8.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.

9.A rectangle has vertices A(0, 0), B(6, 0), C(6, 4) and D(0, 4). Work out the length of the diagonal AC. Give your answer correct to 2 decimal places.

10.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?

11.Work out the distance between the points (−3, 4) and (5, −2).

12.Work out the exact value of (cos 45°)² + (sin 45°)².

13.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.

14.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?

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