Geometry and measures worksheet — GCSE Foundation

1.A solid cone has a base radius of 6 cm and a vertical height of 10 cm. Work out the volume of the cone. Use π = 3.14 and give your answer correct to 1 decimal place.

2.A triangular badge has two sides of length 8 cm and a third side of length 5 cm. Work out the perimeter of the badge.

3.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.

4.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.

5.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?

6.A transversal crosses a pair of parallel lines. At one line, the angle is (5x + 4)°. The corresponding angle at the other line is (3x + 24)°. Work out the value of x.

7.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.

8.An isosceles trapezium has exactly one pair of parallel sides, and its two non-parallel sides are equal in length. How many lines of symmetry does it have?

9.Which of these describes an obtuse angle?

10.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?

11.The column vector r has top number 2 and bottom number 6. Which of these column vectors is parallel to r?

12.A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.

13.Point A has coordinates (2, 5). Point A is translated to point B using the column vector with top number 6 and bottom number −3. Write down the coordinates of point B.

14.A solid pyramid has a square base of side 6 cm. Its apex is directly above the centre of the base, at a vertical height of 8 cm. Work out the volume of the pyramid.

15.A builder lays a low wall made from identical bricks. The diagram shows the plan of the wall's footprint on a grid, where each square is one brick. The wall is built up to a height of 4 bricks everywhere. Work out the total number of bricks used.