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Question

An ant is moving around a few food pieces of different shapes scattered on the floor. For which food piece would the ant have to take a longer round?

Solution
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(a) diameter of semicircle $$=2.8cm$$
$$\therefore$$ Perimeter $$=\pi r+2r=\dfrac{22}7\times 2.8+2\times 2.8=8.8+5.6\ cm=14.4\ cm$$

(b) Total perimeter $$=1.5+1.5+2.8+\pi r$$, where $$r=\dfrac{2.3}2=1.4cm$$
$$=1.5+1.5+2.8+\left(\dfrac{22}7\times 1.4\right)$$
$$=5.8+8.8=14.6\ cm$$

(c) Total perimeter $$=2+2+\pi r$$, where $$r=\dfrac{2.8}2=1.4cm$$
$$=4+8.8=12.8cm$$

Hence, it is clearly seen that the distance of (b) i.e., $$14.6$$ is the longest.

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