# 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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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 = 2πr, where r is the radius of the circle.

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(a)Radius (r) of semi-circular part = (2.8/2)cm = 1.4 cm

Perimeter of the given figure = 2.8 cm + πr

= 2.8 cm + (22/7 x 1.4)cm

= 2.8 cm + 4.4 cm = 7.2 cm

(b) Radius (r) of semi-circular part = (2.8/2)cm = 1.4 cm

Perimeter of the given figure = 1.5 cm + 2.8 cm + 1.5 cm +π (1.4 cm)

= 5.8 cm + 22/7(1.4 cm)

= 5.8 cm + 4.4 cm = 10.2 cm

(c) Radius (r) of semi-circular part = (2.8/2)cm = 1.4 cm

Perimeter of the figure(c) = 2 cm + πr + 2 cm

= 4 cm + 22/7 x (1.4 cm)

= 4 cm + 4.4 cm = 8.4 cm

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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Solution:

i)

Given:

Diameter = 2.8 cm

Perimeter of the figure = Perimeter of Semicircular part + Diameter of the part

= πr + 2r

=(22/7) × (1.4)  + 2.8

= 22× .2 + 2.8 = 4.4+ 2.8

=7.2 cm

ii)

Given :

Diameter = 2.8 cm

Perimeter of the figure = Perimeter of Semi-circular part + 2Length + Breadth

= πr +L+ 2B

= 22/7× 1.4  + 2.8+ 2× 1.5

= 22×.2 + 2.8+ 3
=4.4 + 2.8+ 3

=10.2 cm

iii)

Given :

Diameter = 2.8 cm

Slant height= 2 cm

Perimeter of the shape = Perimeter of Semi-circular part + 2(slant height)

= πr + 2 (slant height)

= 22/7× 1.4  +2+2

=4.4 + 4

=8.4 cm

Hence, the food shape in (b) requires the ant to cover the more distance.

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