Geometry and measures worksheet — GCSE Foundation

1.A solid has one curved surface and two flat circular faces of equal size, one at each end. What is the name of this solid?

2.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.

3.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

4.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.

5.Write down the exact value of tan 45°.

6.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.

7.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.

8.A ramp rises at 30° to the horizontal. Its sloping surface is 4.8 m long. Safety rules say the vertical rise of a ramp must be no more than 2.5 m. Work out how far below that limit the rise of this ramp is.

9.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.

10.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.

11.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.

12.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.

13.The perimeter of a square is 20 cm. Work out the area of the square.

14.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?

15.A solid cylinder is lying on its curved side on a table, with its circular ends facing left and right. What shape is its plan view, looking down from above?