Respuesta :
The grain silo has a circular roof with an area of 803.84ft²
To determine the area of a circle you have to use the following formula:
[tex]A=\pi r^2[/tex]Knowing the area of the circle, you can determine the radius. The first step is to write the formula for the radius (r)
-Divide the area by pi
[tex]\frac{A}{\pi}=r^2[/tex]-Calculate the square root to both sides of the expression
[tex]\begin{gathered} \sqrt[]{\frac{A}{\pi}}=\sqrt[]{r^2} \\ r=\sqrt[]{\frac{A}{\pi}} \end{gathered}[/tex]Replace the expression with A=803.84ft²
[tex]\begin{gathered} r=\sqrt[]{\frac{A}{\pi}} \\ r=\sqrt[]{\frac{803.84}{\pi}} \\ r=\sqrt[]{255.87} \\ r=15.995 \\ r\approx16ft \end{gathered}[/tex]The radius of the silo is around 16ft
To determine the height of the silo you have to use the information of its volume. The volume of a cylinder can be determined using the following formula:
[tex]V=\pi r^2h[/tex]Given that we know the volume and the radius we can use this formula to determine the height, first, write the formula for h:
[tex]\begin{gathered} V=\pi r^2h \\ h=\frac{V}{\pi r^2} \end{gathered}[/tex]We know that V=13665.28ft³ and r=16ft, replace both values on the formula:
[tex]\begin{gathered} h=\frac{13665.28}{\pi(16)^2} \\ h=\frac{13665.28}{256\pi} \\ h=16.99 \\ h\approx17ft \end{gathered}[/tex]The height of the silo is 17ft
