Question

Question 5
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, the 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. $Radius=\frac{Diameter}{2}=\frac{2.8}{2}=1.4cm$
Circumference of semi circle =$\pi r=\frac{22}{7}\times 1.4=4.4cm$
Total distance covered by the ant = Circumference of semi circle + Diameter = 4.4 + 2.8 = 7.2 cm

b. Diameter of semi circle = 2.8 cm
$\therefore Radius=\frac{Diameter}{2}=\frac{2.8}{2}=1.4cm$
Circumference of semi circle = $\pi r=\frac{22}{7}\times 1.4=4.4cm$
Total distance covered by the ant = 1.5 + 2.8 + 1.5 + 4.4 = 10.2 cm

c. Diameter of semi circle = 2.8 cm
$\therefore Radius=\frac{Diameter}{2}=\frac{2.8}{2}=1.4cm$
Circumference of semi circle = $\pi r=\frac{22}{7}\times 1.4=4.4cm$
Total distance covered by the ant = 2 + 2 + 4.4 = 8.4 cm

Hence for figure (b) food piece, the ant would take a longer round