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A cow is tethered to the corner of a rectangular shed.

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A cow is tethered to the corner of a rectangular shed.

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Source: Magoosh



A cow is tethered to the corner of a rectangular shed. If the length of the rope is 5, and the shed has length 4 and width 3, what is the maximum area that is accessible to the cow? (The cow cannot enter the shed).

$$A.\ 12\pi$$
$$B.\ 15\pi$$
$$C.\ 16\pi$$
$$D.\ 18\pi$$
$$E.\ 20\pi$$

The AO is E

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BTGmoderatorLU wrote:
Source: Magoosh



A cow is tethered to the corner of a rectangular shed. If the length of the rope is 5, and the shed has length 4 and width 3, what is the maximum area that is accessible to the cow? (The cow cannot enter the shed).

$$A.\ 12\pi$$
$$B.\ 15\pi$$
$$C.\ 16\pi$$
$$D.\ 18\pi$$
$$E.\ 20\pi$$
Very nice problem! Be sure you understand the figure below:



$$? = {3 \over 4}\pi \cdot {5^2} + {1 \over 4}\pi \cdot {1^2} + {1 \over 4}\pi \cdot {2^2} = {\pi \over 4}\left( {80} \right) = 20\pi $$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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