Solution:

Given data:

Raw material cost = 12 units
Labour cost = 20 units
Direct production cost = 35 units
Other costs = 23 units

To find: Difference between the central angle for the largest and smallest component of the cost of sugar.

Calculation:

Total cost of sugar = Raw material cost + Labour cost + Direct production cost + Other costs
= 12 + 20 + 35 + 23
= 90 units

Now, let's calculate the central angle for each cost component:

Central angle for raw material cost = (Raw material cost/Total cost of sugar) x 360 degrees
= (12/90) x 360
= 48 degrees

Central angle for labour cost = (Labour cost/Total cost of sugar) x 360 degrees
= (20/90) x 360
= 80 degrees

Central angle for direct production cost = (Direct production cost/Total cost of sugar) x 360 degrees
= (35/90) x 360
= 140 degrees

Central angle for other costs = (Other costs/Total cost of sugar) x 360 degrees
= (23/90) x 360
= 92 degrees

Now, let's find the difference between the central angle for the largest and smallest component of the cost of sugar:

The largest central angle is for direct production cost = 140 degrees
The smallest central angle is for raw material cost = 48 degrees

Difference = Largest central angle - Smallest central angle
= 140 - 48
= 92 degrees

Therefore, the difference between the central angle for the largest and smallest component of the cost of sugar is 92 degrees.

Explanation:

Central angle is the angle subtended by an arc at the center of a circle. Here, we have calculated the central angle for each cost component by dividing the cost of each component by the total cost of sugar and multiplying by 360 degrees. The difference between the largest and smallest central angles gives us an idea of the variation in the cost components. In this case, the direct production cost has the largest central angle, indicating that it is the most significant cost component. The raw material cost has the smallest central angle, indicating that it is the least significant cost component. The difference between the largest and smallest central angles is 92 degrees, which means that there is a considerable variation in the cost components.

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