Chapter 11, Problem 13PT

To determine

To calculate the circumference and area of the circle.

Answer to Problem 13PT

Circumference $c=75.4$ feet and area $a=452.6$ square feet.

Explanation of Solution

Given information:

Given figure is a circle with radius $r=12$ feet.

Formula used:

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

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

Here ‘r’ is the radius of the circle.

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

Calculation:

Circumference of a circle.

  $c=2\times \pi \times r$

Formula to compute the circumference of a circle.

  $=2\times \frac{22}{7}\times 12$

Putting the values in the formula.

  $=\frac{528}{7}$

Simplifying the expression.

  $=75.43$

Rounding off to the nearest tenth.

  $c=75.4$ feet.

Area of a circle

  $a=\pi \times r^2$

Formula for the area of a circle.

  $=\frac{22}{7}\times {12}^2$

Putting the values in the formula.

  $=\frac{22}{7}\times 144$

Simplifying the same.

  $=452.57$

Rounding to the nearest tenth.

  $a=452.6$ square feet.