Chapter 11.8, Problem 26PPS

To determine

To compute the diameter of the circle.

Answer to Problem 26PPS

  $6.8$ centimeters.

Explanation of Solution

Given information: Area of the circle $a=35.6$ square centimeters.

Formula used: Area of circle $a=\pi \times r^2$

Calculation: $a=\pi \times r^2$

Rearranging the formula to find radius ‘r’.

  $r^2=\frac{a}{\pi }$

Square rooting both sides of the equation.

  $r=\sqrt{\frac{a}{\pi }}$

Putting the numeric values in the expression.

  $=\sqrt{\frac{35.6\times 7}{22}}$

Taken ‘pi’ as $\frac{22}{7}$

  $=\sqrt{\frac{249.2}{22}}$

Simplifying the fraction.

  $=\sqrt{11.327}$

Taking square root.

  $=3.37$

Rounding to the nearest tenth.

  $=3.4$ centimeters.

Now, diameter $d=2\times r$

  $=2\times 3.4$

  $=6.8$ centimeters.