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Given the area of a circle A = 154 cm2. We will use pi = (22)/(7).

Mathematics

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Answer

r=7 cmr = \text{7 cm}

d=14 cmd = \text{14 cm}

C=44 cmC = \text{44 cm}

Step-by-step solution

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Here's how to solve the problem:

Given the area of a circle A=154 cm2A = 154 \text{ cm}^2. We will use π=227\pi = \frac{22}{7}.

  1. Find the radius (rr).

    The formula for the area of a circle is A=πr2A = \pi r^2.

    154=227r2154 = \frac{22}{7} r^2

    To find r2r^2, multiply both sides by 722\frac{7}{22}:

    r2=154×722r^2 = 154 \times \frac{7}{22} r2=7×7r^2 = 7 \times 7 r2=49r^2 = 49

    Take the square root of both sides to find rr:

    r=49r = \sqrt{49} r=7 cmr = \boxed{\text{7 cm}}
  2. Find the diameter (dd).

    The diameter is twice the radius: d=2rd = 2r.

    d=2×7 cmd = 2 \times 7 \text{ cm} d=14 cmd = \boxed{\text{14 cm}}
  3. Find the circumference (CC).

    The formula for the circumference of a circle is C=2πrC = 2\pi r or C=πdC = \pi d. Using C=πdC = \pi d:

    C=227×14 cmC = \frac{22}{7} \times 14 \text{ cm} C=22×2 cmC = 22 \times 2 \text{ cm} C=44 cmC = \boxed{\text{44 cm}}
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