Ex 11.1, 5 - An ant is moving around a few food pieces of different

Ex 11.1, 5 - Chapter 11 Class 8 Mensuration - Part 2
Ex 11.1, 5 - Chapter 11 Class 8 Mensuration - Part 3
Ex 11.1, 5 - Chapter 11 Class 8 Mensuration - Part 4
Ex 11.1, 5 - Chapter 11 Class 8 Mensuration - Part 5 Ex 11.1, 5 - Chapter 11 Class 8 Mensuration - Part 6 Ex 11.1, 5 - Chapter 11 Class 8 Mensuration - Part 7


Transcript

Question 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 = 2Ο€r, 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 = π·π‘–π‘Žπ‘šπ‘‘π‘’π‘Ÿ/2 = 2.8/2 = 1.4 cm Circumference of semicircular part = 1/2 Γ— Circumference of circle Circumference of semicircular part = 1/2 Γ— 2Ο€r = Ο€ Γ— 1.4 = 22/7 Γ— 14/10 = 22 Γ— 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 + (πΆπ‘–π‘Ÿπ‘π‘’π‘šπ‘“π‘’π‘Ÿπ‘’π‘›π‘π‘’ π‘œπ‘“ π‘π‘–π‘Ÿπ‘π‘™π‘’)/2 = 2.8 + 1.5 + 1.5 + 2πœ‹π‘Ÿ/2 = 2.8 + 3 + πœ‹π‘Ÿ = 5.8 + 22/7Γ—2.8/2 = 5.8 + 22/7Γ—1.4 = 5.8 + 22/7Γ—14/10 = 5.8 + 22Γ—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 = π·π‘–π‘Žπ‘šπ‘‘π‘’π‘Ÿ/2 = 2.8/2 = 1.4 cm Circumference of semicircular part = 1/2 Γ— Circumference of circle Circumference of semicircular part = 1/2 Γ— 2Ο€r = Ο€ Γ— 1.4 = 22/7 Γ— 14/10 = 22 Γ— 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)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.