Maths Sign Sector

Difficulty:
intermediate

Rating:
4-stars

GCSE Marks:
5-marks

GCSE Text:
A new sign is being made from a single rectangular sheet of aluminium. The rectangle is curved into an arc before being attached to a wall. Here is the design of the sign.

maths-sign

a)  What is the area of the aluminium sheet needed to make this sign?

The aluminium costs £25 per m² excluding VAT.

b)  What is the total cost of the aluminium including VAT at 20%?

Suggestions:
This is a good example of a complex question that could appear on a Higher GCSE paper. Students will be expected to notice that the width of the rectangle can only be calculated when considering that the sign is a piece of a circumference of a circle, and the question requires multiple skills to be able to solve it. A knowledge of circles and sectors and area is required to solve this question. It is useful to stress to students that even if they forget circle formulae, there are marks to be had just by calculating the cost per m² including VAT, which is a simple percentage calculation.

Extension Ideas:
Teachers could extend the learning by considering:

  • The word ‘MATHS’ will be cut from the centre of the sign, making a hole. The area of the word ‘MATHS’ is 1.5m².  What percentage of the finished sign will be a hole (to the nearest whole number)?

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