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.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.

3.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.

4.Sam says: '3.2 litres is the same as 320 ml, because you multiply by 100.' Which statement about Sam's claim is correct?

5.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.

6.A circular decoration has a radius of 10 cm. A ribbon costs £0.50 per centimetre and is fixed along the curved edge (the arc) of a sector-shaped section with an angle of 90°. Using π = 3.14, work out the cost of the ribbon for this section.

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

8.Write down the exact value of sin 60°.

9.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.

10.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

11.A vertical line passes through the point (5, 2). Write down the equation of this line.

12.A gardener wants to buy edging trim to go all the way around a circular flower bed with a diameter of 8 m. Work out the length of edging trim needed, using π = 3.14. Give your answer to the nearest metre.

13.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

14.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.

15.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.