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 Cir - Mathematics

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.

Solution

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 xx 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 xx (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.

Concept: Mensuration
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APPEARS IN

NCERT Class 8 Maths Textbook
Chapter 11 Mensuration
Exercise 11.1 | Q 5 | Page 171