Geometry and measures worksheet — GCSE Foundation

1.A circular coin has a diameter of 3 cm. Work out the circumference of the coin. Give your answer in terms of π.

2.Two straight roads cross at a junction. The angle between them, measured with a protractor, is 118°. What is the size of the angle vertically opposite to it?

3.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.

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

5.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.

6.A sector of a circle has an angle of 90° and an area of 78.5 cm². Using π = 3.14, work out the radius of the circle.

7.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.

8.A sector of a circle has radius 9 cm and angle 120°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

9.The point (0, −5) lies on one of the two coordinate axes. Write down which axis this is.

10.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.

11.A circle has a diameter of 24 cm. A sector of this circle has an angle of 90°. Using π = 3.14, work out the area of the sector.

12.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

13.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?

14.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.

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