SOLUTION: We have word problems that we have to take them and use an equation to figure out the answer. COuld you please help me with the following problem? A storage bin for corn consists

Question 96671: We have word problems that we have to take them and use an equation to figure out the answer. COuld you please help me with the following problem? A storage bin for corn consists of a cylindrical section made of wire mesh, surmounted by a conical tin roof. The height of the roof is one-third the entire height of the structure. If the total volume of the structure is 1400 pi ft^3 and its radius is 10 ft, what is its height?
I have tried to make an equation but im not sure if I am heading in the right direction. I took the formula for the cylinder and added it with the forlmula for the cone and set them equall to 1400 pi. Then I was going to solve for h, but i got stuck right there. Thanks!
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
let h=height ... (cylinder volume)+(cone volume)=1400pi

pi(10^2)(2h/3)+(pi(10^2)(h/3))/3=1400pi ... dividing by 100pi gives (2h/3)+(h/3)/3=14

(6h/9)+(h/9)=14 ... 7h=14*9 ... h=18
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