Chapter 11.8, Problem 40STP

a.

To determine

To find the algebraic expression of ‘A’ that could be used to find the radius of the circle.

Answer to Problem 40STP

Radius $r=\sqrt{\frac{a}{\pi }}$

Explanation of Solution

Given information:Area of a circle.

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

Use this to find out the radius, if the area of the circle is provided.

  $r^2=\frac{a}{\pi }$

Taking square root on both sides.

  $r=\sqrt{\frac{a}{\pi }}$

b.

To determine

To find the radius of the circle to the nearest tenth.

Answer to Problem 40STP

Radius $=10.2$ centimeters.

Explanation of Solution

Given information:Area of the circle $=327.6$ square centimeters.

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

Calculation:

Area $a=\pi \times r^2$

Change the left-hand side to ‘r’ to find the radius.

  $r^2=\frac{a}{\pi }$

Take square root on both sides.

  $r=\sqrt{\frac{a}{\pi }}$

Putting the values in this expression.

  $=\sqrt{\frac{327.6\times 7}{22}}$

Taking $\pi =\frac{22}{7}$

  $=\sqrt{104.236}$

Taking square root.

  $=10.21$

Rounded to nearest tenth.

  $=10.2$ centimeters.