A wheel makes 2000 rounds when it covers a distance of 88 km. Find the radius of the wheel? Option 1: 7 m Option 2: 10.5 m Option 3: 14 m Option 4: 21 m

Answer: 7 m. Solution: A wheel completes 2000 full rotations while traveling a total distance of 88 km. When a wheel completes one full rotation, it covers a distance equal to its circumference. Circumference of a circle = 2 r where r is the radius. Total distance covered = 88 km = 88 x 1000 = 88,000 m Number of rotations = 2000 Distance covered in 1 rotation = (88,000)/2000 Distance covered in 1 rotation = 44 m Distance in 1 rotation equals the circumference of the wheel. 2 r = 44 r = 44/(2) r = 44/(2 x 22/7) r = (44 x 7)/(2 x 22) r = 308/44 r = 7 m Therefore, the radius of the wheel is 7 m.

Geometry

Circles

Medium

A wheel makes 2000 rounds when it covers a distance of 88 km. Find the radius of the wheel?

7 m

10.5 m

14 m

21 m

✅ Correct Option: 1

A wheel completes 2000 full rotations while traveling a total distance of 88 km.

When a wheel completes one full rotation, it covers a distance equal to its circumference.

Circumference of a circle $= 2\pi r$ where $r$ is the radius.

Total distance covered $= 88$ km $= 88 \times 1000 = 88,000$ m

Number of rotations $= 2000$

Distance covered in 1 rotation $= \dfrac{88,000}{2000}$

Distance covered in 1 rotation $= 44$ m

Distance in 1 rotation equals the circumference of the wheel.

$2\pi r = 44$

$r = \dfrac{44}{2\pi}$

$r = \dfrac{44}{2 \times \frac{22}{7}}$

$r = \dfrac{44 \times 7}{2 \times 22}$

$r = \dfrac{308}{44}$

$r = 7$ m

Therefore, the radius of the wheel is 7 m.

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