Question

PLEASE I NEED HELP!

Circle A is shown with a central angle marked 30 degrees and the radius marked 5 inches.

Which of the following could be used to calculate the area of the sector in the circle shown above?

π(5in)30 over 360
π(5in)230 over 360
π(30in)25 over 360
π(30in)5 over 360

Answer 1

`\pi (5\: \sf in)^2\left((30^(\circ))/(360^(\circ))\right)`

π(5in)² 30 over 360

Explanation:

`\textsf{Area of a sector of a circle}=\left((\theta)/(360^(\circ))\right) \pi r^2`

(where
`\theta` is the angle and r is the radius)

Given:

• 
  `\theta` = 30°
• r = 5 in

Substituting these values into the equation:

`\begin{aligned}\implies\textsf{Area} &=\left((30^(\circ))/(360^(\circ))\right) \pi \cdot (5\: \sf in)^2\\\\ & = \pi (5\: \sf in)^2\left((30^(\circ))/(360^(\circ))\right)\\\\ & = \pi \cdot 25\:(\sf in^2) \cdot (1)/(12)\\\\ & = (25)/(12) \pi \:(\sf in^2) \\\\ & = 6.54\: \sf in^2\:(nearest\:hundredth) \end{aligned}`

Answer 2

π(5in)² * 30 over 360 can be used to determine sector area.

`\sf sector \ area \ : (\theta)/(360) *\pi *radius^2`

# radius = 5 inches

# angle = 30 degrees

sector area:

`\hookrightarrow \sf (30)/(360) *\pi *5^2`

`\hookrightarrow \sf (1)/(12) *\pi *25`

`\hookrightarrow \sf (25)/(12)\pi`

`\hookrightarrow \sf 6.54 \ inch^2`