NEED HELP ASAP PLEASEA 72° sector in a circle has an area of 16.4π yd².What is the area of the circle?Use 3.14 for pi.Enter your answer as a decimal in the box.

Accepted Solution

Solution : Give that, a 72° sector in a circle ,Area of Sector in a circle = [tex] \pi \times r^{2} \times( \frac{\theta}{360} )\\ \:\: where, r = radius\, of\, the\, circle\ \\ \theta = angle \,in \, degrees [/tex]Suppose radius of circle is r . then Volume of sector of circle [tex] \pi \imes r^{2} \times (\frac{72}{360} )= 16.4\pi\\\\r^{2} = \frac{16.4 \pi}{\pi \times \frac{72}{360} } = \frac{16.4 \times 360}{72} [/tex]Area of a Circle of radius, r, [tex] A = \pi\times r^{2} [/tex]Put [tex] r^{2} = \frac{16.4 \times 360}{\times 72} [/tex]Area of Circle, A = [tex] \pi \times \ \frac{16.4 \times 360}{72} =82 \pi[/tex]given, [tex] \pi =3.14 [/tex][tex] volume =82 \times 3.14 = 257.48 [/tex]Hence, Area of circle= 257.48