Find the circumference of a circle whose area is 24.64 sq m (assume pi = 22/7). What is the circumference (in m)?

Introduction / Context:
This question tests the connection between a circle's area and its circumference. The area formula is A = pi*r^2 and the circumference formula is C = 2*pi*r. Since area is given, we first solve for r by rearranging the area formula. Then we substitute r into the circumference formula. Because pi is specified as 22/7, the values are designed to produce a neat radius. Units also matter: area is in square metres, so radius comes out in metres, and circumference will be in metres.

Given Data / Assumptions:

• Area A = 24.64 sq m
• pi = 22/7
• A = pi*r^2
• C = 2*pi*r

Concept / Approach:
Compute r^2 = A/pi, then r = sqrt(r^2). Finally compute C = 2*pi*r. Keep calculations exact using pi = 22/7.

Step-by-Step Solution:
r^2 = A / pi = 24.64 / (22/7) = 24.64 * 7 / 22 24.64/22 = 1.12, so r^2 = 1.12 * 7 = 7.84 r = sqrt(7.84) = 2.8 m C = 2*pi*r = 2*(22/7)*2.8 C = (44/7)*2.8 = 44*0.4 = 17.6 m So circumference = 17.60 m

Verification / Alternative check:
Check area with r=2.8: A = (22/7)*2.8^2 = (22/7)*7.84 = 22*1.12 = 24.64 sq m, exactly matching the given area. So circumference is consistent.

Why Other Options Are Wrong:
14.64 and 16.36 come from incorrect radius extraction or wrong pi placement. 18.40 comes from using r=2.93 approx or arithmetic slips in 2*pi*r. 15.40 is not compatible with the radius implied by the area.

Common Pitfalls:
Using C = pi*d without finding d, mixing up pi*r^2 and 2*pi*r, or rounding r too early before computing circumference.

Final Answer:
The circumference of the circle is 17.60 m.