A grain silo has a cone shaped spout on the bottom in order to regulate the flow of grain
out of the silo. The diameter of the silo is 8
feet. The height of the cylindrical part of the
silo above the cone spout is 12 feet while the
height of the entire silo is 16 feet.

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How many cubic feet of grain are held in the
cone spout of the silo? How many cubic feet
of grain can the entire silo hold?

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

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step-by-step explanation: