Chapter 11, Problem 14PT

To determine

To calculate the circumference and area of the circle.

Answer to Problem 14PT

Circumference $c=\text{33}\text{.9}$ meters and area $a=91.7$ square meters.

Explanation of Solution

Given information:

Given figure is a circle with diameter $d=10.8$ meters. Hence radius $r=\frac{d}{2}$

  $=\frac{10.8}{2}$

  $=5.4$ meters.

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.

  $=2\times \frac{22}{7}\times 5.4$

Putting the values in the formula.

  $=\frac{237.6}{7}$

Simplifying the expression.

  $=\text{33}\text{.94}$

Rounding off to the nearest tenth.

  $c=\text{33}\text{.9}$ meters.

Area of a circle

  $a=\pi \times r^2$

Formula for the area of a circle.

  $=\frac{22}{7}\times {5.4}^2$

Putting the values in the formula.

  $=\frac{22}{7}\times \text{29}\text{.16}$

Simplifying the same.

  $=\frac{\text{641}\text{.52}}{7}$

Further dividing the numerator by the denominator.

  $=\text{91}\text{.65}$

Rounding to the nearest tenth.

  $a=91.7$ square meters.