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Question

A rope by which cow is tethered is increased from $$\displaystyle 16 \ m $$ to $$\displaystyle 23 \ m$$. How much additional ground dows it have now to graze?

Solution
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At radius = $$\displaystyle 16 \ m$$, cow can graze the area of plot is $$\displaystyle \pi r^2 = \frac{22}{7} \times 16 \times 16 = 804.5 \ m^2$$
At radius = $$\displaystyle 23 \ m$$, cow can graze the area of plot is $$\displaystyle \pi r^2 =\frac{22}{7} \times 23 \times 23= 1662.57 \ m^2$$
Additional ground area =$$\displaystyle 1662.57 - 804.5 = 858 \ m^2$$

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