Find the length of the arc of a circle whose central angle is 90° and whose radius is 3.5 cm. (Use π = 22/7 and express the answer in centimetres.)

Introduction / Context:
This is a basic arc length problem from circle geometry. The length of an arc depends on the radius of the circle and the measure of the central angle that subtends the arc at the centre. When the central angle is given in degrees, we can directly use the fraction of the full circumference corresponding to that angle. This type of calculation is very common in aptitude tests involving sectors and arcs of circles.

Given Data / Assumptions:
- Radius r of the circle is 3.5 cm. - Central angle θ is 90°. - π is taken as 22 / 7. - We must find the length of the arc corresponding to the 90° central angle.

Concept / Approach:
The full circumference of a circle is given by C = 2 * π * r. An angle of 360° corresponds to the full circumference. Therefore, an angle of θ degrees corresponds to a fraction θ / 360 of the full circumference. Hence, the arc length s for a central angle θ is s = (θ / 360) * 2 * π * r. Here θ = 90°, which is exactly one quarter of 360°, so the arc length is one quarter of the full circumference. This gives a quick and simple calculation.

Step-by-Step Solution:
Step 1: Write the formula for arc length when the angle is in degrees: s = (θ / 360) * 2 * π * r. Step 2: Substitute θ = 90°, r = 3.5 cm, and π = 22 / 7 into the formula. Step 3: So s = (90 / 360) * 2 * (22 / 7) * 3.5. Step 4: Simplify 90 / 360 to 1 / 4. Step 5: The expression becomes s = (1 / 4) * 2 * (22 / 7) * 3.5. Step 6: Compute 2 * 3.5 = 7, so s = (1 / 4) * (22 / 7) * 7. Step 7: The factor 7 cancels with the denominator 7, giving s = (1 / 4) * 22. Step 8: Compute (1 / 4) * 22 = 22 / 4 = 5.5 cm. Step 9: Therefore the length of the arc is 5.5 centimetres.

Verification / Alternative check:
We can also reason that 90° is one quarter of a full circle. The full circumference is C = 2 * π * r = 2 * (22 / 7) * 3.5. Since 3.5 = 7 / 2, we have C = 2 * (22 / 7) * (7 / 2) = 22 cm. One quarter of 22 cm is 22 / 4 = 5.5 cm, matching the value obtained from the formula. This confirms that the calculations are consistent and the arc length is correct.

Why Other Options Are Wrong:
Option 11 cm equals half of the full circumference and would correspond to a 180° central angle, not 90°. Option 16.5 cm would correspond to three quarters of the circumference, that is 270°, which is not the angle given. Option 22 cm is the full circumference of the circle, which corresponds to 360°, not to 90°.

Common Pitfalls:
Some learners mistakenly use θ in radians without converting or mix degree and radian formulas. Others may forget to divide by 360 and directly multiply θ with 2 * π * r. Always remember that when θ is in degrees, the correct fraction of the circumference is θ / 360. Breaking the calculation into clear steps and simplifying fractions such as 90 / 360 early helps prevent arithmetic mistakes.

Final Answer:
The length of the required arc is 5.5 cm.