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Assertion (A) : The distribution of land in Pacific Housing Society is shown in the pie chart below. The total land area for project is 144000 m2.

The distribution of land in Pacific Housing Society is shown in the pie chart below. The total land area for project is 144000 m2. Data Handling, Concise Mathematics Solutions ICSE Class 8.

The ratio of the area kept open to the ratio of the area for apartment construction is 5 : 13.

Reason (R) : In a pie chart, the central angle of a sector suspended by its arc is proportional to the value it represents.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are incorrect.

  3. A is true, but R is false.

  4. A is false, but R is true.

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Answer

In a pie chart, the central angle of a sector suspended by its arc is proportional to the value it represents.

So, reason (R) is true.

Area kept open = 90°360°×144000\dfrac{90°}{360°} \times 144000

Area for apartment construction = 234°360°×144000\dfrac{234°}{360°} \times 144000

Ratio =90°360°×144000234°360°×144000=90°234°=513.\text{Ratio } = \dfrac{\dfrac{90°}{360°} \times 144000}{\dfrac{234°}{360°} \times 144000} \\[1em] = \dfrac{90°}{234°} \\[1em] = \dfrac{5}{13}.

So, assertion (A) is true.

∴ Both A and R are correct, and R is the correct explanation for A.

Hence, option 1 is the correct option.

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