Geometry and measures worksheet — GCSE Foundation

1.A cylindrical candle and a cone-shaped candle have the same base radius and the same height. State the cone's volume as a fraction of the cylinder's volume.

2.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.

3.A cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?

4.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

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

6.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?

7.In this question, a curved surface counts as a face. How many faces does a cone have?

8.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

9.Point A is at (5, 2). It is translated by the vector (−3, 4) to give point A′. Work out the coordinates of A′.

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

11.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?

12.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.

13.Two straight lines AB and CD cross at point O. Angle AOC = 74°. Work out angle AOD.

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

15.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.