Geometry and measures worksheet — GCSE Foundation

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

2.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

3.A bead starts at position (2, −1) on a grid, in centimetres. It is moved by the column vector u, with top number 3 and bottom number 5, and then moved by the column vector v, with top number −7 and bottom number 2. Work out the coordinates of the bead's final position.

4.Which of the following correctly describes what it means for two lines to be perpendicular?

5.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?

6.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

7.A support strut for a shed roof is in the shape of a right-angled triangle. The two shorter sides of the strut are 5 m and 9 m. Work out the length of the sloping strut (the hypotenuse). Give your answer correct to 1 decimal place.

8.In triangle ABC and triangle DEF, the angle at A equals the angle at D, and AB ÷ DE = AC ÷ DF. Write down what this proves about the two triangles.

9.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.

10.A sector of a circle has radius 5 cm and angle 72°. Work out the arc length of the sector, in terms of π.

11.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.

12.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.

13.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

14.Two similar triangular tiles have lengths in the ratio 3 : 5. The longest side of the smaller tile is 9 cm. Work out the length of the longest side of the larger tile.

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