The pie-chart given below shows the annual agricultural production. Area under cultivation in state A is 1200 sq.kms. Area under cultivation in state B is 1800 sq.kms.
Question: 1
What is the total area in which Rice is grown in both states together?
Show Hint
For pie-chart problems, first convert the sector angle into a fraction of \(360^\circ\), then multiply by the total quantity represented.
Concept:
In a pie chart,
\[
\text{Area represented}
=
\frac{\text{Sector Angle}}{360^\circ}
\times
\text{Total Area}.
\]
Step 1: Find rice cultivation area in State A.
Rice angle in State A:
\[
60^\circ.
\]
Total cultivated area:
\[
1200 \text{ sq. kms}.
\]
Therefore,
\[
\frac{60}{360}\times1200
=
\frac{1}{6}\times1200
=
200.
\]
Thus rice area in State A is
\[
200 \text{ sq. kms}.
\]
Step 2: Find rice cultivation area in State B.
Rice angle in State B:
\[
80^\circ.
\]
Total cultivated area:
\[
1800 \text{ sq. kms}.
\]
Hence
\[
\frac{80}{360}\times1800
=
400.
\]
Thus rice area in State B is
\[
400 \text{ sq. kms}.
\]
Step 3: Find total area.
\[
200+400=600.
\]
Therefore the total area under rice cultivation is
\[
\boxed{600 \text{ sq. kms}}.
\]
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Question: 2
What is the difference in the area of pulses grown in both states?
Show Hint
When comparing sectors from different pie charts, always compute actual values first; comparing angles directly can be misleading because totals are different.
Step 1: Calculate pulses area in State A.
Angle for pulses:
\[
54^\circ.
\]
Hence
\[
\frac{54}{360}\times1200
=
180.
\]
Therefore,
\[
\text{Pulses area in State A}
=
180 \text{ sq. kms}.
\]
Step 2: Calculate pulses area in State B.
Angle for pulses:
\[
50^\circ.
\]
Hence
\[
\frac{50}{360}\times1800
=
250.
\]
Therefore,
\[
\text{Pulses area in State B}
=
250 \text{ sq. kms}.
\]
Step 3: Find the difference.
\[
250-180
=
70.
\]
Thus the difference is
\[
\boxed{70 \text{ sq. kms}}.
\]
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Question: 3
Identify the state and crop which is grown in the maximum area.
Show Hint
In pie-chart questions involving multiple charts, convert every sector into its actual quantity before making comparisons.
Step 1: Compute the areas corresponding to the given options.
Vegetables in State A:
\[
\frac{44}{360}\times1200
=
146.67
\]
sq. kms.
Vegetables in State B:
\[
\frac{90}{360}\times1800
=
450
\]
sq. kms.
Sugarcane in State A:
\[
\frac{105}{360}\times1200
=
350
\]
sq. kms.
Rice in State B:
\[
\frac{80}{360}\times1800
=
400
\]
sq. kms.
Step 2: Compare the values.
\[
146.67,\quad 450,\quad 350,\quad 400.
\]
The largest value is
\[
450.
\]
Step 3: Conclusion.
Therefore the crop grown in the maximum area is
\[
\boxed{\text{Vegetables in State B}}.
\]
