SubjectCover

Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter

Shape and Space 9

17 practice questions

Start practising (4 questions)

Practice questions

1–4 of 4 · Hard

  1. Question 1

    2 marks · Hard

    In the prism shown, the base is a rectangle measuring 6 cm by 8 cm, and the height (the perpendicular distance between the two rectangular faces) is 5 cm. Work out, to 3 significant figures, the angle that the longest diagonal of the prism makes with the base.

    Geometry diagram with points A, B, C, D, EBase ABCDABCDE
    Rectangular prism: Rectangle base ABCD with AB = 8 cm, BC = 6 cm. Height (vertical distance from base to top face) = 5 cm. Diagonal AE from A on base to E on the top face, above D.
    Answer and see the solution →

  2. Question 2

    4 marks · Hard

    A cuboid has sides of lengths 7 cm, 9 cm, and 15 cm. Calculate the length of the space diagonal (from one corner to the farthest opposite corner), giving your answer to 3 significant figures.

    Geometry diagram with points A, B, C, D, E, FABCDF
    Cuboid: length = 7 cm, width = 9 cm, height = 15 cm; diagonal joins vertex A (0, 0, 0) to vertex F (7, 9, 15).
    Answer and see the solution →

  3. Question 3

    4 marks · Hard

    A square-based pyramid has a base of side 10 cm. The vertex V is vertically above the centre of the base and is 14 cm above the centre. Explain, step by step, how trigonometry can be used to calculate the angle between a slant edge (V to one corner of the base) and the base. You may use a diagram to support your answer.

    Geometry diagram with points P, Q, R, S, O (centre), V (above centre)PQRSO (centre)
    Square-based pyramid with base PQRS, side 10 cm, vertex V above base centre, height 14 cm, slant edge VP.
    Answer and see the solution →

  4. Question 4

    5 marks · Hard

    The diagram shows a cuboid with length 12 cm, width 7 cm, and height 20 cm.

    Geometry diagram with points A, B, C, D, E (above A)ABCD
    Cuboid: Length = 12 cm (from A to B), width = 7 cm (from B to C), height = 20 cm (from A to E vertically above A).

    (a) Calculate the length of the diagonal from A to the opposite vertex G (the space diagonal).

    (b) Calculate the angle between the diagonal AG and the base ABCD. Give your answer to 3 significant figures.

    (a)

    Calculate the length of the space diagonal AG.

    [2 marks]
    (b)

    Calculate the angle between AG and the base ABCD. Give your answer to 3 significant figures.

    [3 marks]
    Answer and see the solution →