Question 1 - Page 87 - Shortest Paths on a Cube - Chapter 4 Class 8 - Exploring Some Geometric Themes (Ganita Prakash II

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Question 1 - Page 87 What is the length of the shortest path between the ant and the laddu?Now, we can unfold our Cuboid in 2 ways Let’s try it out Since both are straight lines, we find shortest distance in both cases The lower value is our actual shortest Distance In First case, Shortest Distance = 42 cm In Second Case And it is the Hypotenuse of a right triangle with sides 24 cm And, 32 cm Thus, by Pythagoras Theorem (Shortest Distance)2 = 322 + 242 (Shortest Distance)2 = 1024 + 576 (Shortest Distance)2 = 1600 (Shortest Distance)2 = 402 Canceling square both sdies Shortest Distance = 40 cm Since 40 cm is shorter than 42 cm – we use the 2nd net The book's final question asks: "What does this show?" It shows that you cannot trust your eyes when looking at a 3D object. To truly find the shortest path, you have to imagine multiple different ways of unfolding the net, draw a straight line on each one, and do the math to see which straight line is actually the shortest!