Respuesta :
We have been given that the shape of the storage shed is in the form of Cone.
It has been given that the shed sits 12 feet above the ground and it holds 51.4 cubic feet of salt.
So basically we've been given:
Height [tex]=h=12 ft[/tex]
Volume[tex]=51.4 ft^3[/tex]
So using the formula for the volume of cone, we get:
[tex]V=\frac{1}{3} \pi r^2 h[/tex], where 'h' is the height of the cone, V is the volume, and 'r' is the radius of the cone.
Plugging the values of height and volume in the equation we get:
[tex]51.4=\frac{1}{3} \pi r^2(12)[/tex]
Solving for 'r', we get:
[tex]r^2=\frac{3 \times 51.4}{12\times\pi}=4.092[/tex]
[tex]r^2=4.092[/tex]
[tex]r=\sqrt{4.092}=2.02[/tex]
Therefore, the radius of the cone is 2.02 or 2 feet.
