Question

What is the area of a sector with radius 10" and measure of arc equal to 45°?

help me please

Answer 1

see circle area is pir^2 which is pix100....when theta = 90 its quarter pi25 is the area but 45 is half so the area must be 25/2*pi

Answer 2

Sorry, writing the final answer:
\[45°=\frac{\pi}{4}rad\]
\[A=\frac{\theta \times r^2}{2}\]
With theta in radians
\[A=\frac{\pi \times 100}{2 \times 4}=\frac{25\times \pi}{2}\]
in square inches

Answer 3

\[\frac{x}{{\pi}r^2} = \frac{45}{360}\]
\[\frac{x}{{\pi}10^2} = \frac{45}{360}\]

Answer 4

Cross Multiply, solve for x

Answer 5

\[360x = 4500\pi \]

\[x = \frac{4500{\pi}} {360} \]

Answer 6

x = 39.2 units squared

Answer 7

or x = 25pi/2 units squared