Question

Please answer question 11, 12, And 13 there different word problems.

Answer 1

radius= 12 meters

Step-by-step explanation

11)the area of the sector is given by:

`A=(5)/(18)\pi r^2`

where r is the radius ( in meters)

then

Step 1

Let

`\begin{gathered} \text{radius}=r \\ \text{Area}=\text{ A=}40\pi(m^2) \end{gathered}`

now replace and solve for r

`\begin{gathered} A=(5)/(18)\pi r^2 \\ 40\pi=(5)/(18)\pi r^2 \\ \text{the }\pi\in\text{ both sides is eliminated,so} \\ 40=(5)/(18)r^2 \\ \text{now,multiply both sides by 18/5} \\ 40\cdot(18)/(5)=(5)/(18)r^2\cdot(18)/(5) \\ 144=r^2 \\ \text{square root in both sides} \\ √(144)=√(r^2) \\ 12=r \end{gathered}`

therefore, the answer is

radius= 12 meters

I hope this helps you