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The front and side elevations of a prism, with a pentagon as its cross section, are drawn on this one-centimetre square grid - OCR - GCSE Maths - Question 13 - 2017 - Paper 1
Question 13
The front and side elevations of a prism, with a pentagon as its cross section, are drawn on this one-centimetre square grid. (a) Draw accurately the plan of the pr... show full transcript
Worked Solution & Example Answer:The front and side elevations of a prism, with a pentagon as its cross section, are drawn on this one-centimetre square grid - OCR - GCSE Maths - Question 13 - 2017 - Paper 1
Step 1
Draw accurately the plan of the prism on the grid below
Answer
To draw the plan of the prism, first analyze the provided side and front elevations. The base of the prism is a rectangle with the dimensions determined from the drawing. The base is wider than the height of the prism.
- Identify Dimensions: From the given elevations, identify the base width (6 cm) and height (4 cm) of the rectangle representing the pentagon cross-section.
- Draw Rectangle: Using the grid, draw a rectangle with a base of 6 cm and a height of 4 cm. Ensure that this representation is clear and fits within the confines of the grid.
- Mark Edges: Ensure all edges and relevant lines are dark and well-defined for clear visibility.
Step 2
Calculate the volume of the prism
Answer
To calculate the volume of the prism, use the formula for the volume of a prism:
- Calculate Base Area: The area of the pentagon cross-section is 9 cm², as noted in the marking scheme.
- Determine Height: The height of the prism from the front elevation is identified to be 6 cm.
- Substitute Values: Substitute the area and height into the formula:
- Final Answer: Therefore, the volume of the prism is 54 cm³.