Discussion
A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?
Answer: C
The calf grazes a circle, so the extra ground is the ring between the old and new radii.
\[ \Delta A = \pi\left(R^{2} - r^{2}\right) = \frac{22}{7}\left(23^{2} - 12^{2}\right) \]
\[ = \frac{22}{7}(529 - 144) = \frac{22}{7} \times 385 \]
\[ = 22 \times 55 = 1210 \text{ m}^{2} \]
The difference of the squares is needed, not the square of the difference: \( \pi(23-12)^{2} = 380 \) m² is a quite different and much smaller area.
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