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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

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 314 for class=

Respuesta :

calculista

Answer:

[tex]95.5\ ft^2[/tex]

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

[tex]\frac{2\pi r }{360^o}=\frac{10}{30^o} \\\\r=\frac{360(10)}{2(3.14)(30)}\\\\r= 19.1\ ft[/tex]

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

[tex]\frac{\pi r^{2}}{360^o}=\frac{x}{30^o}\\\\x=\frac{3.14(19.1^2)(30)}{360}\\\\x=95.5\ ft^2[/tex]

akposevictor

The area of the sector which represents the lawn irrigated by the sprinkler is: [tex]\mathbf{ 95.5 $ ft^2}[/tex]

Recall:

  • Area of sector = [tex]\frac{\theta}{360} \times \pi r^2[/tex]
  • Length of arc = [tex]\frac{\theta}{360} \times 2 \pi r[/tex]

Given:

[tex]\theta = 30^{\circ}[/tex]

length of arc = 10 feet

First, find the radius using the length of arc formula.

[tex]\frac{\theta}{360} \times 2 \pi r[/tex]

  • Substitute

[tex]10 = \frac{30}{360} \times 2 \times 3.14 \times r\\\\10 = 0.52r\\\\r = \frac{10}{0.52} \\\\r = 19.2[/tex]

radius = 19.2 ft

Find the area of the sector:

Area of sector = [tex]\frac{\theta}{360} \times \pi r^2[/tex]

  • Substitute

[tex]= \frac{30}{360} \times \times 3.14 \times 19.2^2\\\\\mathbf{= 95.5 $ ft^2}[/tex]

The area of the sector which represents the lawn irrigated by the sprinkler is: [tex]\mathbf{ 95.5 $ ft^2}[/tex]

Learn more here:

https://brainly.com/question/14117642

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