A household wants to understand exactly where its weekly income goes. The pie chart below shows how the weekly budget is divided between four spending categ...
Question 1 Report
A household wants to understand exactly where its weekly income goes. The pie chart below shows how the weekly budget is divided between four spending categories, with the angle of each sector marked on the diagram.
- Write down the fraction of the budget spent on Bills. Give your answer in its simplest form. (1)
- The weekly budget is £300. Work out the amount spent on Rent. (2)
Answer Details
This question tests converting an angle on a pie chart into a fraction of the whole, since a full circle is \(360^\circ\).
(a) The sector for Bills has an angle of \(60^\circ\). As a fraction of the full \(360^\circ\):
\[\frac{60}{360} = \frac{1}{6}.\][1]
(b) The Rent sector has an angle of \(120^\circ\), representing a fraction \(\frac{120}{360}\) of the budget. Applying this to the weekly budget of £300:
\[\frac{120}{360} \times 300 = £100.\][2]
The underlying idea is that any sector's angle out of \(360^\circ\) gives its fraction of the whole pie chart, which can then be applied to the total amount the chart represents.
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