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Difficulty: MediumData Representation and Charts

A pie chart illustrates the annual allocation of funds for an agricultural research station across four sectors: Crop Research, Livestock, Irrigation, and Equipment Maintenance. The sector angles for Crop Research, Livestock, and Irrigation are 135∘135^\circ, 90∘90^\circ, and 60∘60^\circ respectively. If the total annual budget is N7,200,000\text{N}7,200,000, what is the amount allocated to Equipment Maintenance in Naira?

Answer: 1500000 Naira

Answer

The amount allocated to Equipment Maintenance is 1,500,000 Naira.
A complete pie chart has a total angle of 360∘360^\circ, representing the full amount of N7,200,000\text{N}7,200,000. The angle corresponding to Equipment Maintenance is 360∘−(135∘+90∘+60∘)=75∘360^\circ - (135^\circ + 90^\circ + 60^\circ) = 75^\circ. The dollar/naira allocation is given by 75∘360∘×7,200,000=1,500,000\frac{75^\circ}{360^\circ} \times 7,200,000 = 1,500,000.

Step-by-Step Solution

1
Calculate the sum of the given sector angles
Sum of known angles = 285 degrees
Determining the total angular measure already accounted for by the three known sectors.
2
Subtract the sum of known angles from 360 degrees
Sector angle for Equipment Maintenance = 75 degrees
The sum of all sector angles in a pie chart is always 360 degrees.
3
Multiply the fraction of the pie chart by the total funds
1,500,000 Naira
Converting the sector angle representation to its corresponding quantitative value.

Key Concept

Pie chart sector angle computation and value conversion
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Topics

Data Representation and Charts

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