Volume of a Silo?

Question

I'm having a lot of trouble solving this word problem! Please help!

A silo is composed of a right circular cylinder with a right circular cone on the top of the cylinder that has the same radius. The height of the cone is half the height of the cylinder and the circumference of the cylinder is 20pi feet.

a.) Write the volume of the silo in terms of the height of the cylinder, h.

b.) If you want the volume of the silo to be 700 cubic feet, what should be the total height of the silo?

 

Thank you!!

Answer 1

Let the Radius of the cylinder be r

Circumference of the cylinder = 2∏ r = 20 ∏

                                                    r = 20∏ /2∏  

                                                      = 10 feet

Now let height of the cylinder be h,

So the height of the cone will be h'= h/2

 

a) Volume of the silo = Volume of the cylinder + volume of the cone

                           = ∏ r² h +  ∏ r² h'/3

                           = ∏ r² h + ∏ r² ( h/2 )/3

                           = ∏ r2 h + ∏ r² h /6

                          =(7/6 ) ∏ r² h

 

b) Volume of silo =(7/6 ) ∏ r² h = 700 ,solve and find the value of h  and so the total height of the silo will be ( h+ h/2)