A nation's total federal budget of ₦500\text{ billion} is allocated across four key sector… — JAMB UTME

A nation's total federal budget of $₦500\text{ billion}$ is allocated across four key sectors: Health ( $₦125\text{ billion}$ ), Education ( $₦175\text{ billion}$ ), Defense ( $₦120\text{ billion}$ ), and Agriculture (the remainder). In a pie chart constructed to represent this budget distribution, what is the central angle (in degrees) representing the allocation for Agriculture?

Answer: 57.6 degrees

Answer

The central angle representing the allocation for Agriculture is

57.6^\circ

To calculate the central angle of a sector in a pie chart, find the ratio of that sector's value to the total value and multiply by

360^\circ

. Subtracting the specified sector allocations (

₦125\text{ billion} + ₦175\text{ billion} + ₦120\text{ billion} = ₦420\text{ billion}

) from the total budget of

₦500\text{ billion}

leaves

₦80\text{ billion}

for Agriculture. The proportion is

\frac{80}{500} = 0.16

. Multiplying

0.16

360^\circ

results in a central angle of

57.6^\circ

Step-by-Step Solution

Calculate the monetary allocation for the Agriculture sector.

Agriculture allocation =

₦80\text{ billion}

The total budget is

₦500\text{ billion}

, and the combined allocation for Health, Education, and Defense is

₦125 + ₦175 + ₦120 = ₦420\text{ billion}

Find the fractional share of Agriculture relative to the entire budget.

Proportional share =

0.16

(or

16\%

Dividing

₦80\text{ billion}

by the total budget of

₦500\text{ billion}

gives

\frac{80}{500} = 0.16

Convert the fractional share into a sector angle in degrees.

Central angle =

57.6^\circ

A full circle in a pie chart corresponds to

360^\circ

, so

0.16 \times 360^\circ = 57.6^\circ

Key Concept

Pie Chart Central Angle Calculation

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