Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 9
105 practice questions
Topics covered
Practice questions
61–70 of 105
Question 61
3 marks · Normal
Answer and see the solution →A cuboid has dimensions 6 cm × 8 cm × 10 cm. Using Pythagoras’ theorem, explain how to find the length of its longest diagonal.
Question 62
4 marks · Normal
Answer and see the solution →The diagram shows a rectangular box. The base AB = 9 cm, BC = 5 cm, and the height is BE = 12 cm. Point F is directly above C.
(a)[2 marks]Find the length AF.
(b)[2 marks]Find the angle that AF makes with the base ABCD.
Question 63
2 marks · Normal
Answer and see the solution →For a square-based pyramid with base edge of 10 cm and height of 15 cm (vertex directly above the centre), work out the vertical angle (angle between a side face and the base).
Question 64
3 marks · Normal
Answer and see the solution →A right triangular prism has end triangle sides 3 cm, 4 cm and 5 cm, and height (length perpendicular to end) of 10 cm.
Calculate the length of the longest diagonal from one vertex to the opposite vertex on the other end.
Question 65
3 marks · Normal
Answer and see the solution →In a solid with a rectangular base 7 cm × 10 cm, a point P is vertically above the centre of the base at a height of 12 cm. Explain how you would use trigonometry to find the angle between the edge from P to a base corner and the base plane.
Question 66
4 marks · Normal
Answer and see the solution →The diagram shows a rectangular box (cuboid) with length 7 cm, width 5 cm and height 12 cm.
Diagram of cuboid ABCDEFGH Calculate the length of the diagonal from point A to point G (opposite corners of the box). Give your answer correct to 3 significant figures.
Question 67
2 marks · Hard
Answer and see the solution →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.
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. Question 68
4 marks · Hard
Answer and see the solution →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.
Cuboid: length = 7 cm, width = 9 cm, height = 15 cm; diagonal joins vertex A (0, 0, 0) to vertex F (7, 9, 15). Question 69
4 marks · Hard
Answer and see the solution →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.
Square-based pyramid with base PQRS, side 10 cm, vertex V above base centre, height 14 cm, slant edge VP. Question 70
5 marks · Hard
Answer and see the solution →The diagram shows a cuboid with length 12 cm, width 7 cm, and height 20 cm.
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)[2 marks]Calculate the length of the space diagonal AG.
(b)[3 marks]Calculate the angle between AG and the base ABCD. Give your answer to 3 significant figures.