4024/21 Oct/Nov 2022, Question 11: Volume of a Pyramid
Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 8 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Regular pentagon ABCDE has centre O, side AB = 6 cm and OA = d cm. Show d = 5.10 cm to 2 decimal places, then find the volume of the pyramid with this base and sloping edges 14 cm.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 3 marks
Show that the distance from the centre O to a vertex of the regular pentagon with side 6 cm is d = 5.10 cm, correct to 2 decimal places.
- 1Angle at centre AOB = 360 ÷ 5 = 72°
- 2Triangle OAB is isosceles; the line from O to the midpoint of AB bisects angle AOB, giving 36°
- 3sin 36° = 3/d
- 4d = 3 ÷ sin 36° = 5.1039…
- 5d = 5.10 cm (2 d.p.)
Answer5.103 to 5.104
Part (b) · 5 marks
For the pyramid with regular pentagon base ABCDE, vertex F above O and each sloping edge 14 cm, calculate the volume.
- 1Height h: 14² = h² + 5.10²
- 2h = √(14² − 5.10²) = 13.038…
- 3Base area = 5 × 1/2 × 5.10 × 5.10 × sin 72° = 61.84…
- 4Volume = 1/3 × 61.84… × 13.038…
- 5= 268.8… ≈ 269 cm³
Answer269 or 268.5 to 269.2
Stuck on a step? Read the free lesson: Volume of a Pyramid
Practise more volume of a pyramid questions
Real 4024 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on volume of a pyramid
Also searched as: 4024/21/O/N/22 · 4024_w22_qp_21 · 4024 w22 21 · question 11.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.