Wheel radius from travel distance and revolutions:\nA wheel makes 1000 revolutions while covering 88 km without slipping. Find the wheel’s radius (in metres).

Difficulty: Easy

14
13
12
11
None of these

Correct Answer: 14

Explanation:

Introduction / Context:
When a wheel rolls without slipping, the linear distance traveled equals the number of revolutions times the circumference. From total distance and revolutions, we can find the circumference and then the radius.

Given Data / Assumptions:

Total distance D = 88 km = 88,000 m.
Number of revolutions n = 1000.
Circumference C = 2πr.

Concept / Approach:
Compute the circumference per revolution as D / n, then solve for r from 2πr = C.

Step-by-Step Solution:

C = D / n = 88,000 m / 1000 = 88 m per revolution.2πr = 88 ⇒ r = 88 / (2π) = 44 / π.Using π ≈ 22/7 ⇒ r = 44 / (22/7) = 44 * 7 / 22 = 14 m.

Verification / Alternative check:

Circumference 2π * 14 ≈ 88 m; 1000 such revolutions cover 88,000 m = 88 km.

Why Other Options Are Wrong:

13, 12, 11 m produce circumferences not matching 88 m, hence total distance differs from 88 km.

Common Pitfalls:

Forgetting to convert km to m; using diameter instead of radius in the 2πr formula.

Wheel radius from travel distance and revolutions:\nA wheel makes 1000 revolutions while covering 88 km without slipping. Find the wheel’s radius (in metres).

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