Question

A man riding a bicycle completes one lap of a circular field along its circumference at the speed of 14.4 km/hr in 1 minute 28 seconds. What is the area of the field?

• A. \(7958\) sq m
• B. \(9856\) sq m
• C. \(8842\) sq m
• D. \(8958\) sq m
• E. \(7856\) sq m

Answer 1

The Correct Option is B

Concept:

• Circumference = speed $\times$ time
• Area = \(\pi r^2\)

Step 1: Convert units.
\[ 14.4 \text{ km/hr} = 4 \text{ m/s} \] \[ 1 \text{ min } 28 \text{ sec} = 88 \text{ sec} \]
Step 2: Circumference.
\[ = 4 \times 88 = 352 \text{ m} \]
Step 3: Find radius.
\[ 2\pi r = 352 \Rightarrow r = \frac{352}{2\pi} = \frac{176}{\pi} \] Taking \(\pi = \frac{22}{7}\): \[ r = \frac{176 \times 7}{22} = 56 \]
Step 4: Area.
\[ \pi r^2 = \frac{22}{7} \times 56^2 = 9856 \]
Step 5: Option analysis.

• (A) Incorrect $\times$
• (B) Correct \checkmark
• (C) Incorrect $\times$
• (D) Incorrect $\times$
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (B).