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A circular playground has an area of 616 m². Find the radius of the playground. Use pi = (22)/(7).

Mathematics

ScanSolve AI Answer

Answer

14 m\text{14 m}

Step-by-step solution

4 steps
  1. Identify the given information and the formula for the area of a circle.

    The area of the circular playground (AA) is 616 m2616 \text{ m}^2.
    The formula for the area of a circle is A=πr2A = \pi r^2, where rr is the radius.
    We will use the approximation π=227\pi = \frac{22}{7}.

  2. Substitute the given area into the formula.

    616=227r2616 = \frac{22}{7} r^2
  3. Solve for r2r^2.

    Multiply both sides by 722\frac{7}{22}:

    r2=616×722r^2 = 616 \times \frac{7}{22} r2=616×722r^2 = \frac{616 \times 7}{22}

    Divide 616 by 22:

    616÷22=28616 \div 22 = 28 r2=28×7r^2 = 28 \times 7 r2=196r^2 = 196
  4. Find the radius rr by taking the square root of r2r^2.

    r=196r = \sqrt{196} r=14r = 14

    The radius of the playground is 14 meters.

    The final answer is 14 m\text{14 m}.

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