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?

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Figure a

Figure b

Figure c

all are same

answer is B.

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Detailed Solution

It is given an ant is moving around a few food pieces of different shapes scattered on the floor and figure.
Question Image

Given figure (a):
Circumference of food-piece (a) = circumference of semicircle + diameter
Question Image

As radius of circle (R) = half of the diameter,

R = \frac{2.8}{2} cm

Circumference =

πR

π 2.8 2 = 4.4 cm

Perimeter (a) = 4.4+ 2.8 = 7.2cm…………(i)
Given figure (b):
Question Image

List the corner points of the food-piece as A, B, C and D
AB = CD = 1.5 cm
And BC = 2.8 cm
Total perimeter of the food-piece

⇒ A B + B C + C D + c i r c u m f e r e n c e 2 ⇒ 1.5 + 2.8 + 1.5 + π × 2.8 2 ⇒ 10.2 cm

Hence, perimeter of food-piece (b) =10.2cm………. (ii)
Given figure (c):
Question Image

Perimeter of food-piece (c) = (Circumference of semicircular part + 2 + 2)
As radius (R) = half of diameter,

R = \frac{2.8}{2} cm

Circumference of semicircular part =

(π R)

π × 2.8 2 = 4.4 cm

Hence, perimeter of food-piece (c) = (4.4 + 2+2) cm = 8.4cm………(iii)
The food-piece with the greatest perimeter will subject the ant to take the longest round.
Comparing (i), (ii) and (iii), the perimeter of the food-piece (b) is the greatest, therefore the ant will take the longest round around the food piece (b).
Hence option (2) is correct.

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