Chapter 6
Measuring Space: Perimeter and Area
CBSE Class 9
Mathematics Solutions
Educart Mathematics class Class 9 NCERT Exemplar cover
Question:

What is the difference in radius between the first and second lanes? Use given figure to find the stagger needed by the runner in the second lane. Will an equal stagger be needed between the third and second lanes?                                                                                                                                                                                                                                               [Page No. 127]

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Answer: Verified

The width of each lane is 1.22 m, so the running line of the second lane has a radius that is 1.22 m more than that of the first lane. Hence, the difference in radius is 1.22 m.

Stagger for the second lane: Over one lap the two bends make a full circle, so the extra distance the second-lane runner would cover is 2π×1.22=2×3.1416×1.22=7.672\pi \times 1.22 = 2 \times 3.1416 \times 1.22 = 7.67 m.

So, the runner in the second lane should start about 7.67 m ahead of the runner in the first lane.

Between the third and second lanes the difference in radius is again one lane width, 1.22 m, so the extra distance is again 2π×1.22=7.672\pi \times 1.22 = 7.67 m. Yes, an equal stagger is needed. In fact, the stagger between every pair of adjacent lanes is the same, which is exactly why the staggers continue uniformly out to the last lane.

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