Geometry and measures worksheet — GCSE Foundation

1.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.

2.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.

3.A party hat is in the shape of a cone with a base radius of 6 cm and a slant height of 10 cm. Work out the curved surface area of the party hat. Use π = 3.14 and the formula curved surface area = πrl.

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

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

6.A photocopier enlarges a document so that every length is multiplied by the same scale factor. A line on the original document is 3.2 cm long, and the same line measures 11.2 cm on the enlarged copy. A second line on the original document is 2.5 cm long. Work out the length of the second line on the enlarged copy, giving your answer to 2 decimal places.

7.A room measures 4.2 m by 3.6 m. A flooring company needs the area in cm² to order the right amount of vinyl flooring. Work out the area of the room in cm².

8.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.

9.A garden plan is drawn to a scale of 1 cm : 1.8 m. A path on the plan measures 4.5 cm. What is the real length of the path, in metres, to 1 decimal place?

10.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

11.A submarine travels due south. What is the three-figure bearing for this direction?

12.A solid metal sphere has a radius of 5 cm. It is melted down and recast into a solid cylinder with the same radius, 5 cm. Work out the height of the cylinder, so that its volume equals the volume of the sphere. Use π = 3.14 and give your answer correct to 1 decimal place.

13.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

14.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.

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