A circle has circumference 26.4 cm.\nFind its exact area (in square centimetres).

Difficulty: Easy

55.44
44.55
33.44
44.33

Correct Answer: 55.44

Explanation:

Introduction / Context:
Relating circumference to area requires computing the radius from C = 2 * pi * r, then substituting into A = pi * r^2. Using the common fraction pi = 22/7 keeps arithmetic exact here.

Given Data / Assumptions:

C = 26.4 cm.
Use pi ≈ 22/7 for clean ratios.

Concept / Approach:
Find r from C = 2 * pi * r, then compute A = pi * r^2.

Step-by-Step Solution:

r = C / (2 * pi) = 26.4 / (2 * 22/7) = 26.4 * 7 / 44 = 4.2 cmA = pi * r^2 = (22/7) * (4.2)^2 = (22/7) * 17.64 = 22 * 2.52 = 55.44 cm^2

Verification / Alternative check:
Back-compute: With r = 4.2, C = 2 * pi * r = 2 * (22/7) * 4.2 = 26.4 cm; consistent.

Why Other Options Are Wrong:
They correspond to incorrect r values due to arithmetic or pi substitution errors.

Common Pitfalls:
Using pi ≈ 3 or 3.14 without keeping consistency across both computations, leading to rounding drift.

A circle has circumference 26.4 cm.\nFind its exact area (in square centimetres).

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