Cart A has a wheel radius of 10 cm and travels 10 km. Cart B has a wheel radius of 12 cm and makes the same number of revolutions as Cart A. How far does Cart B travel? Express the answer in kilometres.

hard 4 marks Class 4 · Mathematics · Carts and Wheels

Answer

12 km

The correct answer is 12 km — 6. Convert back to kilometres: 1,200,000 cm = 12,000 m = 12 km.

Step-by-step solution

1. Circumference of Cart A = 2πr = 20π cm.
2. Convert 10 km to cm: 10 km = 1,000,000 cm.
3. Number of revolutions N = distance / circumference = 1,000,000 / (20π) = 50,000/π.
4. Circumference of Cart B = 2π(12) = 24π cm.
5. Distance by Cart B = N × 24π = (50,000/π) × 24π = 1,200,000 cm.
6. Convert back to kilometres: 1,200,000 cm = 12,000 m = 12 km.

Common mistake: Not converting units or misapplying circumference formula

Concept tested: Radius and distance relationship