Q. 54.3( 281 Votes )

# 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.

A. B.

C.

Answer :

Food pieces with larger perimeter would make the ant to take the longer round.

**Perimeter for Shape A:**

Since, Shape A is Semi Circle.

Also diameter is the part of the figure.

Perimeter = πr + Diameter

= πr + 2r

= (22/7) × 1.4 + 2.8

= 7.2 cm

**Perimeter for Shape B: **

Perimeter = Sum of length of all the outer boundary

= 2.8 + 1.5 + 1.5 + Perimeter of semi circular part

= 2.8 + 1.5 + 1.5 + πr

= 2.8 + 1.5 + 1.5 + (22/7) × 1.4

= 10.2 cm

**Perimeter for Shape C: **

Perimeter = Sum of length of all the outer boundary

Perimeter = 2 + 2 + perimeter of semi circular part

Radius of semicircle = d/2

= 2.8/2

= 1.4 cm

= 2 + 2 + πr

Perimeter = 2 + 2 + (22/7) × 1.4

= 8.4 cm

∴ Perimeter is maximum for shape B, So Ant would have to take the longer round for Shape B.

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