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? Remember, circumference of a circle can be obtained by using the expression $c=2\pi r$, where $r$ is the radius of the circle.

Answer 1

(a) Radius ($r$) of semi-circular part $=\frac{2.8}{2}=1.4cm$

Perimeter of the given figure $=2.8cm+\pi r$

$=2.8+\frac{22}{7}\times 1.4$

$=2.8+4.4$

$=7.2cm$

(b)Radius ($r$) of semi-circular part $=\frac{2.8}{2}=1.4cm$

Perimeter of the given figure $=1.5+2.8+1.5+\pi \left(1.4\right)$

$=5.8+\frac{22}{7}\left(1.4\right)$

$=5.8+4.4$

$=10.2cm$

(c) Radius ($r$) of semi-circular part $=\frac{2.8}{2}=1.4cm$

Perimeter of the figure(c) $=2+\pi r+2$

$=4+\frac{22}{7}\left(1.4\right)$

$=4+4.4$

$=8.4cm$

Thus, the ant will have to take a longer round for the food-piece (b), because the perimeter of the figure given in alternative (b) is the greatest among all.
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