Chapter 11, Problem 17PT

a.

To determine

To find: The area of the mural.

Answer to Problem 17PT

The balance in the annuity after $10$ years $=17563.9365$

Explanation of Solution

Given: The diameter of mural is $50\mathrm{ft}$ .

Calculation: The diameter of mural is $50\mathrm{ft}$ .

Radius of the mural $=\frac{50}{2}=25\mathrm{ft}$ .

Area of the mural:

  $\begin{array}{l}=\pi r^2\\ =\frac{22}{7}\times 25\times 25\\ =\frac{13750}{7}{\mathrm{ft}}^2\\ =1964.29{\mathrm{ft}}^2\end{array}$

Thus, the area of the mural $1964.29{\mathrm{ft}}^2$ .

b.

To determine

To find:The area of the sector.

Answer to Problem 17PT

The area of the sector is $207.34f{t}^2$ .

Explanation of Solution

Given:Given radius is $25\mathrm{ft}$ and central angle is ${38}^{\circ }$ .

Calculation:

Area of sector:

  $\begin{array}{l}=\frac{\theta }{{360}^{\circ }}\pi r^2\\ =\frac{{38}^{\circ }}{{360}^{\circ }}\times \frac{22}{7}\times 25\times 25\\ =207.34f{t}^2\end{array}$

Thus, the area of the sector is $207.34f{t}^2$ .