In order to find out how many cubic feet of grain are held in the cone spout of the silo, we need to find out the volume of the cone spout of the silo.
We know that : Volume of a cone is given by = 1/3πr²h
Given : Diameter of the silo is 8 feet
As Radius is half the Diameter, Radius (r) = 4 feet
From the figure, we can notice that Height of the cone spout of the silo is given by subtracting Height of the cylindrical part of the silo from the Height of the entire silo.
⇒ Height of the cone spout of the silo = 16 - 12 = 4 ft
Substituting the values in the volume of the cone formula, we get :
⇒ Volume of the cone spout of the silo = 1/3 × π × 4² × 4
⇒ Volume of the cone spout of the silo = 67 ft³
⇒ Cone spout of the silo can hold 67 ft³ of grain
In order to find how many feet of grain can the entire silo can hold, we need to find the volume of the cylindrical part of the silo.
We know that : Volume of a cylinder is given by = πr²h
From the figure, we can notice that :
Radius (r) = 4 ft
Height (h) = 12 ft
⇒ Volume of the Cylindrical part of the silo = π × 4² × 12
⇒ Volume of the Cylindrical part of the silo = 603.2 ft³
We can notice that :
Volume of the Entire silo = Volume of the Cone spout + Volume of the Cylinder part
⇒ Volume of the Entire silo = 67 + 603.2 = 670.2 ft³
⇒ Entire silo can hold 670.2 ft³ of grain
