Chapter 11.9, Problem 32SR

To determine

To calculate the circumference and area of the circle.

Answer to Problem 32SR

Circumference $29.9$ feet and area $70.9$ square feet.

Explanation of Solution

Given information:

Diameter $d=9\frac{1}{2}$

  $=\frac{19}{2}$ feet.

Formula used:

Circumference of circle $c=2\times \pi \times r$

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

Where ‘r’ is the radius of the circle.

For calculation, value of $\pi =\frac{22}{7}$ .

Calculation:

Radius $r=\frac{d}{2}$

  $=\frac{19}{2}\times \frac{1}{2}$

On simplifying

  $=\frac{19}{4}$ feet.

Circumference of circle

  $c=2\times \pi \times r$

Formula for circumference.

  $=2\times \frac{22}{7}\times \frac{19}{4}$

Putting the value of radius ‘r’.

  $=\frac{11\times 19}{7}$

On simplifying the expression

  $=\frac{209}{7}$

On dividing the numerator by the denominator

  $=29.86$

Rounding the result to the nearest tenth.

  $=29.9$ feet.

Area of circle

  $a=\pi \times r^2$

Formula for area

  $=\frac{22}{7}\times {\left(\frac{19}{4}\right)}^2$

Putting the value of ‘r’ in the expression.

  $=\frac{22}{7}\times \frac{19}{4}\times \frac{19}{4}$

On further simplification

  $=\frac{3971}{56}$

On dividing the numerator by denominator.

  $=70.91$

Rounding the result to the nearest tenth.

  $=70.9$ square feet.