Ex 11.1, 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, circumference of a circle can be obtained by using the expression c = 2πr, where r is the radius of the circle.
Here,
We need to find circumference of all 3 figures and find the greatest of them
Let’s find it one by one
Circumference of (a)
So,
Circumference of (a) = Circumference of semicircular part + Diameter
Circumference of semicircular part
Radius = 𝐷𝑖𝑎𝑚𝑡𝑒𝑟/2
= 2.8/2 = 1.4 cm
Circumference of semicircular part = 1/2 × Circumference of circle
Circumference of semicircular part = 1/2 × 2πr
= π × 1.4
= 22/7 × 14/10
= 22 × 2/10
= 44/10
= 4.4 cm
Now,
Circumference of (a) = Circumference of semicircular part + Diameter
= 4.4 + 2.8
= 7.2 cm
Circumference of (b)
Lets mark the figure with points A, B, C and D
By symmetry of the figure
AB = CD = 2.8 cm
AD = BC = 1.5 cm
Now,
Distance moved = AB + BC + AD + (𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒)/2
= 2.8 + 1.5 + 1.5 + 2𝜋𝑟/2
= 2.8 + 3 + 𝜋𝑟
= 5.8 + 22/7×2.8/2
= 5.8 + 22/7×1.4
= 5.8 + 22/7×14/10
= 5.8 + 22×2/10
= 5.8 + 44/10
= 5.8 + 4.4
= 10.2 cm
So, perimeter is 10.2 cm
Circumference of (c)
Now,
Circumference of (c) = Circumference of semicircular part + 2 + 2
Circumference of semicircular part
Radius = 𝐷𝑖𝑎𝑚𝑡𝑒𝑟/2
= 2.8/2 = 1.4 cm
Circumference of semicircular part = 1/2 × Circumference of circle
Circumference of semicircular part = 1/2 × 2πr
= π × 1.4
= 22/7 × 14/10
= 22 × 2/10
= 44/10
= 4.4 cm
Now,
Circumference of (c) = Circumference of semicircular part + 2 + 2
= 4.4 + 2 + 2
= 8.4 cm
Since perimeter of part (b) is highest
Thus, Ant will have longest round in case (b)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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