The slant height of cone L=6.3ft
Base radius is5.9/2 =2.95ft
The volume of a cone is given by
[tex]\frac{1}{3}\Pi r^2h[/tex]
where h= the vertical height of the cone, r=base radius
to find the vertical height, we use Pythagoras theorem
[tex]\begin{gathered} l^2=h^2+r^2 \\ 6.3^2=h^2+2.95^2 \end{gathered}[/tex][tex]\begin{gathered} 39.69=h^2+8.70 \\ h^2=39.69-8.70 \end{gathered}[/tex][tex]\begin{gathered} h^2=30.99 \\ \text{taking the square root of both side} \\ h=5.57ft \end{gathered}[/tex][tex]\text{volume of cone =}\frac{1}{3}\times3.14\times2.95^2\times5.57[/tex][tex]\begin{gathered} =\frac{1}{3}\times3.14\times8.70\times5.57 \\ =\frac{1}{3}\times152.16 \\ =50.72 \end{gathered}[/tex]
The volume of the cone is 51.0ft³
The right option is the Third one
