Geometry and measures worksheet — GCSE Foundation

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

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

3.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?

4.A sector of a circle has radius 7 cm and angle 90°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

5.A sector has an angle of 45°. Priti says: 'The area of the sector is one eighth of the area of the full circle, whatever the radius is.' Is Priti correct?

6.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.

7.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

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

10.A right-angled triangle has a hypotenuse of 8 cm, and one of its shorter sides is 4 cm. Work out the size of the angle between that 4 cm side and the hypotenuse.

11.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.

12.A sector of a circle has radius 6 cm and angle 60°. Work out the arc length of the sector, in terms of π.

13.A sector of a circle has radius 4 cm and angle 90°. Using π = 3.14, work out the area of the sector.

14.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

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