JAMB 2020 Mathematics · Question 39

In preparing rice cutlets, a cook used 75g of rice, 40g of margarine, 105g of meat and 20g of bread crumbs…

Question

In preparing rice cutlets, a cook used 75g of rice, 40g of margarine, 105g of meat and 20g of bread crumbs. Find the angle of the sector which represent meat in a pie chart?

A.30 $^o$
B.60 $^o$
C.112.5 $^o$
D.157.5 $^o$

Answer: D. 157.5 $^o$

Explanation written with AI and checked against the answer key

To solve this problem, we need to determine the proportion of the total weight that the meat represents and then convert that proportion into degrees for a pie chart.

1. Analyze the question

We are given the weights of four ingredients used to make rice cutlets. We need to find the sector angle for the meat in a pie chart. A full circle (pie chart) represents $360^\circ$ .

2. Explain the concept

To find the angle of a sector for a specific item, use the formula:

\text{Sector Angle} = \left( \frac{\text{Weight of the item}}{\text{Total weight of all items}} \right) \times 360^\circ

3. Show the solution

Step 1: Calculate the total weight of all ingredients.

\text{Total weight} = 75\text{g (rice)} + 40\text{g (margarine)} + 105\text{g (meat)} + 20\text{g (bread crumbs)}

\text{Total weight} = 240\text{g}

Step 2: Calculate the fraction represented by the meat.

\text{Fraction of meat} = \frac{\text{Weight of meat}}{\text{Total weight}}

\text{Fraction of meat} = \frac{105}{240}

Step 3: Convert the fraction to degrees.

\text{Angle} = \left( \frac{105}{240} \right) \times 360^\circ

Simplify the calculation:

\text{Angle} = 105 \times \left( \frac{360}{240} \right)

\text{Angle} = 105 \times 1.5

\text{Angle} = 157.5^\circ

4. Identify the answer

Comparing our result to the given options: A. $30^\circ$ B. $60^\circ$ C. $112.5^\circ$ D. $157.5^\circ$

The calculated value matches option D.

5. Tip

When dealing with pie chart questions, always check if your total angle adds up to $360^\circ$ . If you are ever unsure of your calculation, remember that the sector angle is simply the "share" of the total. If the meat is roughly half of the total weight (105 is slightly less than half of 240), your answer should be slightly less than $180^\circ$ (half of $360^\circ$ ). This helps you quickly eliminate impossible options!

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