Multiple choice

The pie diagrams on the monthly expenditure of two families A and B are drawn with radii of two circles taken in the ratio 16 : 9 to compare their expenditures. Which of the following is the appropriate data used for the above mentioned pie diagrams?

  1. Rs. 16,000 and Rs. 9,000

  2. Rs. 8,000 and Rs. 4,500

  3. Rs. 25,600 and Rs. 8,100

  4. Rs. 4,000 and Rs. 3,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The area of a pie chart is proportional to the square of the radius. Ratio of areas = (16/9)^2 = 256/81. Thus, the expenditures must be in the ratio 256:81. 25600:8100 matches this.

AI explanation

The area of a circle, which represents the total expenditure in a pie chart, is proportional to the square of its radius. The radii are given in the ratio 16:9, so the ratio of their areas (and thus their expenditures) must be 16^2 : 9^2, which is 256 : 81. Applying this ratio to the given values, Rs. 25,600 and Rs. 8,100 simplifies exactly to 256 : 81, making it the appropriate data used for the pie diagrams.

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