Question

The sector shows the area of a lawn that will be watered by a sprinkler. What is the area, rounded to the nearest tenth? Use 3.14 for

Answer 1

Answer:

$95.5\ ft^2$

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

A circumference of the circle subtends a central angle of 360 degrees

so

using proportion

$\frac{2\pi r }{360^o}=\frac{10}{30^o} \\\\r=\frac{360(10)}{2(3.14)(30)}\\\\r= 19.1\ ft$

step 2

Find the area of sector

we know that

The area of the circle subtends a central angle of 360 degrees

so using proportion

Let

x ----> the area of the sector

$\frac{\pi r^{2}}{360^o}=\frac{x}{30^o}\\\\x=\frac{3.14(19.1^2)(30)}{360}\\\\x=95.5\ ft^2$