Chapter 11, Problem 15PT

To determine

To calculate the area of the remaining pizza.

Answer to Problem 15PT

  $154.7$ squareinches.

Explanation of Solution

Given information:

Diameter of pizza $d=15$ inches.

Formula used:

Area of sector of circle $a=\pi \times r^2\times \frac{\theta }{360°}$ . Where ‘r’ is the radius of the circle.

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

Calculation:

Radius of the circle $r=\frac{d}{2}$ where ‘d’ is the given diameter.

  $=\frac{15}{2}$

Putting the value of ‘d’.

  $=7.5$ inches

  $a=\pi \times r^2\times \frac{\theta }{360°}$

Formula of area of the sector of a circle.

Here, $\theta =360°-45°$

Since the missing slice have a central angle of $45°$

Hence $\theta =315°$

  $=\frac{22}{7}\times {7.5}^2\times \frac{315°}{360°}$

Putting the values in the formula for area of the sector of a circle.

  $=\frac{22}{7}\times 56.25\times \frac{35}{40}$

Dividing the measures of the angles by 9.

  $=22\times 56.25\times \frac{1}{8}$

Dividing the measures of the angles by 7 and 5.

  $=154.69$

Rounding off the result to the nearest tenth.

  $=154.7$ square inches.