GCSE OCR Maths Constructions: The diagram shows a square-based

The diagram shows a square-based pyramid ABCDE - OCR - GCSE Maths - Question 14 - 2023 - Paper 6

Question 14

The diagram shows a square-based pyramid ABCDE. O is the centre of the base. The pyramid has base length 20cm and each sloping edge has length 14.5cm: (a) Draw the... show full transcript

Worked Solution & Example Answer:The diagram shows a square-based pyramid ABCDE - OCR - GCSE Maths - Question 14 - 2023 - Paper 6

Step 1

Draw the base of the pyramid

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Answer

To start drawing the plan view, the base ABCD is a square. Since the length of the base is 20 cm, this translates to 5 cm on the grid (as 1 cm on the grid represents 4 cm in reality). Thus, sketch a square of 5 cm with corners labeled A, B, C, and D.

Step 2

Locate the center point O

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Answer

The center O of the square base is found by marking the midpoint of the sides. This will be at the coordinates (2.5 cm, 2.5 cm) on the grid.

Step 3

Draw the sloping edges

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Answer

The sloping edges from each vertex (A, B, C, D) to the apex E of the pyramid, which is directly above point O, should be marked. The height from O to E can be calculated using the Pythagorean theorem. Since the sloping edge is 14.5 cm, the perpendicular height can be calculated as follows:

Let the height be h.

Using the formula: $h = \sqrt{(14.5)^2 - (10)^2} = \sqrt{210.25 - 100} = \sqrt{110.25} \approx 10.5 cm$

On the grid, this distance represents approximately 2.625 cm. Draw lines from O to points A, B, C, and D at the calculated height.

Step 4

Label the plan view

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Answer

Ensure all points are clearly labeled: A, B, C, D for the base corners, and O for the center of the base. Additionally, mark the apex E above the central point O at the calculated height.

The diagram shows a square-based pyramid ABCDE - OCR - GCSE Maths - Question 14 - 2023 - Paper 6

Worked Solution & Example Answer:The diagram shows a square-based pyramid ABCDE - OCR - GCSE Maths - Question 14 - 2023 - Paper 6

Draw the base of the pyramid

Locate the center point O

Draw the sloping edges

Label the plan view

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