Chapter 11.8, Problem 25PPS

To determine

To find the area of sector of cross-section of the trunk.

Answer to Problem 25PPS

  $837.4$ squarefeet.

Explanation of Solution

Given information: Circumference $c=102.6$ feet.

Formula used: Area of circle $A=\pi \times r^2$ and, circumference of circle $c=2\times \pi \times r$ to compute the radius ‘r’.

Calculation: $c=2\times \pi \times r$

  $r=\frac{c}{2\times \pi }$

Putting the value of ‘c’.

  $=\frac{102.6}{2\pi }$ feet.

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

  $=\pi \times \frac{102.6}{2\pi }\times \frac{102.6}{2\pi }$

Putting the value of radius/

  $=\frac{102.6}{2}\times \frac{102.6\times 7}{2\times 22}$

Divide ‘pi’ from the numerator and denominator, and taken ‘pi’ as $\frac{22}{7}$ .

  $=\frac{73687.32}{88}$

Divide the numerator by the denominator.

  $=837.36$

Rounding to the nearest tenth.

  $=837.4$ square feet.