Chapter 11, Problem 24SGR

a.

To determine

To find: The area of the pizza that charlie eat.

Answer to Problem 24SGR

The area of the pizza that charlieeat is $201.12{\mathrm{inch}}^2$ .

Explanation of Solution

Given: Charlie and kris ordered a $16inch$ pizza that have $12$ slides.

Calculation: Charlie and kris ordered a $16inch$ pizza that have $12$ slides.

Central angle:

  $\begin{array}{l}=\frac{{360}^{\circ }}{12}\\ ={30}^{\circ }\end{array}$

Area of one piece=Area of sector:

  $\begin{array}{l}=\frac{\theta }{{360}^{\circ }}\pi r^2\\ =\frac{{30}^{\circ }}{{360}^{\circ }}\times \frac{22}{7}\times 16\times 16\\ =67.04{\mathrm{inch}}^2\end{array}$

Charlie ate three piece so area of three piece :

  $\begin{array}{l}=3\times 67.04\\ =201.12{\mathrm{inch}}^2\end{array}$

Thus, the area of the pizza that charlie eat is $201.12{\mathrm{inch}}^2$ .

b.

To determine

To find: The area of the pizza that kris eat.

Answer to Problem 24SGR

The area of the pizza that kris eat is $134.08{\mathrm{inch}}^2$ .

Explanation of Solution

Given: Charlie and kris ordered a $16inch$ pizza that have $12$ slides.

Calculation: Charlie and kris ordered a $16inch$ pizza that have $12$ slides.

Central angle:

  $\begin{array}{l}=\frac{{360}^{\circ }}{12}\\ ={30}^{\circ }\end{array}$

Area of one piece=Area of sector:

  $\begin{array}{l}=\frac{\theta }{{360}^{\circ }}\pi r^2\\ =\frac{{30}^{\circ }}{{360}^{\circ }}\times \frac{22}{7}\times 16\times 16\\ =67.04{\mathrm{inch}}^2\end{array}$

Charlie ate two pieces.

Kris ate three pieces.

Remaining pieces $=12-3-2=12-5=7$ .

Area of seven pieces:

  $\begin{array}{l}=7\times 67.04\\ =469.28{\mathrm{inch}}^2\end{array}$

Thus, the area of remaining pizza is $469.28{\mathrm{inch}}^2$ .

c.

To determine

To find:The area of left pizza.

Answer to Problem 24SGR

The area of the pizza that charlieeat is $201.12{\mathrm{inch}}^2$ .

Explanation of Solution

Given: Charlie and kris ordered a $16inch$ pizza that have $12$ slides.

Calculation: Charlie and kris ordered a $16inch$ pizza that have $12$ slides.

Central angle:

  $\begin{array}{l}=\frac{{360}^{\circ }}{12}\\ ={30}^{\circ }\end{array}$

Area of one piece=Area of sector:

  $\begin{array}{l}=\frac{\theta }{{360}^{\circ }}\pi r^2\\ =\frac{{30}^{\circ }}{{360}^{\circ }}\times \frac{22}{7}\times 16\times 16\\ =67.04{\mathrm{inch}}^2\end{array}$

Charlie ate three piece so area of three piece :

  $\begin{array}{l}=3\times 67.04\\ =201.12{\mathrm{inch}}^2\end{array}$

Thus, the area of the pizza that charlie eat is $201.12{\mathrm{inch}}^2$ .